Systems and methods for coded-aperture-based correction of aberration obtained from Fourier ptychography

ABSTRACT

Certain embodiments pertain to techniques for coded-aperture-based correction of sample-induced and system-induced aberration.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority and benefit of U.S. Provisional Patent Application No. 62/723,374, titled “Characterizing and Correcting for Sample-Induced Optical Aberration Using Coded-Aperture-Based Correction of Aberration Obtained From Fourier Ptychography,” and filed on Aug. 27, 2018; this application is a continuation-in-part of U.S. patent application Ser. No. 15/620,674, filed on Jun. 12, 2017 and titled “PUPIL PTYCHOGRAPHY METHODS AND SYSTEMS,” which claims priority to U.S. Provisional Patent Application No. 62/348,433, titled “Characterizing the Aberration of an Optical System with Spatially Incoherent Light Using Pupil Ptychography” and filed on Jun. 10, 2016; each of these applications is hereby incorporated by reference in its entirety and for all purposes.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Grant No. EY026228 awarded by the National Institutes of Health. The government has certain rights in the invention.

FIELD

Certain embodiments described herein are generally related to digital imaging, and more specifically, to coded-aperture-based aberration correction in optical imaging.

BACKGROUND

A perfect aberration-free optical lens simply does not exist. Broadly speaking, much of optical imaging system design tends to focus on selecting specialized optical elements and their spatial relationships to minimize aberrations to provide an acceptable image resolution over a desired field-of-view. The more optical surfaces that are available, the greater the extent to which the aberrations can be minimized. There are, however, limitations to the number of optical elements that can be supported within the confines of an objective. Moreover, this design strategy for minimizing aberration cannot be expected to accomplish completely zeroing out aberrations. The issue of aberrations in simpler optical systems with fewer optical surfaces is even more pronounced. The eye is a good example of such an optical system where the optical quality of the human eye lens and cornea is rather poor. The aberrations in the eye lens and cornea need to be corrected or compensated for in order to get an image of the retinal layer with high enough resolution for diagnostic purposes.

SUMMARY

Implementations pertain to a computationally aberration compensating imaging system comprising an imager, an optical system, and one or more processors and memory. The optical system comprises an aperture modulator configured to modulate apertures at the Fourier plane of the imager, and one or more optical elements configured to propagate incoherent light from a sample being imaged to the aperture modulator and propagate light from the aperture modulator to the imager. The imager is configured to acquire a plurality of coded-aperture images, a plurality of limited-apertures, and a full pupil image. The one or more processors and memory are configured to use the plurality of limited-aperture images to recover a pupil function of the optical system and correct for sample-induced and system-induced aberration by deconvolving the full pupil image and the plurality of coded-aperture images using the recovered pupil function to determine a substantially aberration-free image.

Implementations pertain to a computationally aberration compensating imaging method comprising receiving, from an imager, a plurality of coded-aperture images, a plurality of limited-aperture images, and a full pupil image, using the plurality of limited-aperture images to recover a pupil function of a system in an optical path between a sample being imaged and the imager, and correcting for sample-induced and system-induced aberration by deconvolving the full pupil image and the plurality of coded-aperture images using the recovered pupil function to determine a substantially aberration-free image.

These and other features are described in more detail below with reference to the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a simplified block diagram of a pupil ptychography imaging system, according to various implementations.

FIG. 2 is a schematic diagram of components of a pupil ptychography imaging system implemented for retinal imaging, according to embodiments.

FIG. 3 is a schematic diagram of components of a pupil ptychography imaging system implemented for retinal imaging, according to embodiments.

FIG. 4 is a schematic diagram of components of a pupil ptychography imaging system implemented for imaging of a natural scene, according to embodiments.

FIG. 5 depicts a flowchart of operations of a pupil ptychography method, according to various implementations.

FIG. 6 depicts a flowchart of operations of an aberration characterization process of a pupil ptychography method, according to an implementation.

FIG. 7 is a simplified block diagram of a CACAO-FP system, according to various implementations.

FIG. 8 is a schematic diagram of certain optical elements of a CACAO-FP system, according to various implementations, and an unknown lens and a sample being imaged by the CACAO-FP system.

FIG. 9 is the general imaging pipeline for a CACAO-FP imaging method, according to various implementations.

FIG. 10 is a schematic diagram of components of a CACAO-FP system, according to one implementation.

FIG. 11 is a schematic diagram of components of a CACAO-FP system, according to a light sheet fluorescence microscopy implementation.

FIG. 12 depicts a flowchart of operations of a CACAO-FP imaging method performed by a CACAO-FP system, according to various implementations.

FIG. 13 depicts a flowchart of operations of an example of a deconvolution process with iterative Tikhonov regularization, according to one aspect.

FIG. 14 depicts a flowchart of operations of an example of a blur estimation process for determining local PSFs from limited-aperture images, according to one aspect.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the presented embodiments. The disclosed embodiments may be practiced without one or more of these specific details. In other instances, well-known operations have not been described in detail to avoid unnecessarily obscuring the disclosed embodiments. While the disclosed embodiments will be described in conjunction with the specific embodiments, it will be understood that it is not intended to limit the disclosed embodiments.

Section I—Pupil Ptychography Systems and Methods

A. Introduction to Retinal Imaging

High-resolution retinal imaging can significantly improve the quality of diagnosis, disease progression tracking and assessment of therapy in a broad range of retinal diseases including, for example, retinal degenerations (retinitis pigmentosa), macular telangiectasis, macular dystrophies, age-related macular degeneration (AMD), and inflammatory diseases. Some of these diseases are prevalent (AMD afflicts 12% of the population aged 80+, and retinitis pigmentosa is the most common cause of blindness/low-vision in adults 20-60 years old) and progress slowly, which drives the need for a cost-effective imaging solution that can be broadly deployed for screening and tracking purposes. The availability of new therapeutics further drives this need for a cost-effective imaging solution since the ability to discern the exact impact of the drugs at the cell level is highly useful in informing clinicians about the course of treatments.

Accounting for the numerical aperture of the eye as set by a nominal pupil diameter of 6 mm, an imaging system should be able to focus light to a diffraction-limited spot of size of 1.9 microns on the retina (630 nm wavelength) except that aberrations in the eye actually result in a much poorer focus spot. Some retinal imaging techniques correct for aberrations by including a corrective physical optical arrangement to compensate for the aberrations before acquiring images. This conventional strategy is the basis of the adaptive optics work that was first started in astronomy and that has been applied to ophthalmic imaging systems, in particular confocal scanning laser ophthalmoscopes (cSLO). Conventional adaptive optics scanning laser ophthalmoscopes (AOSLO) have significant limitations that have hindered their broad clinical use. First, the field of view of adaptive optics corrected images tends to be very small oftentimes only 1 degree in size. Since retinal diseases can occupy large portions of the macula and retina, conventional adaptive optics techniques requires multiple images to be obtained and montaged and increases the acquisition time. Long acquisition times are generally impractical for routine clinical use, especially with eye motion from the patient. This requires high-speed tracking systems since adaptive optics requires feedback to keep the aberration correction current. Second, the uneven topology of many retinal diseases presents a major challenge because regions not in the focal plane of the optics will appear out of focus. Third, despite reductions in the cost of certain components, such as deformable mirrors, these conventional systems still remain expensive, limiting their commercial feasibility.

Fourier ptychography is a resolution-enhancement imaging technique that can be applied to a conventional 4f optical arrangement to increase the system's effective numerical aperture, remove the inherent optical aberrations in the system, and allow for quantitative phase measurement of a sample. Details of the Fourier ptychography imaging technique are described in G. Zheng, R. Horstmeyer and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photonics, 2013, which is hereby incorporated by reference in its entirety. Fourier ptychography typically uses the aberration characterization technique referred to as the Embedded Pupil Function Recovery (EPRY) method, which is described in X. Ou, G. Zheng and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Optics Express, 2014, which is hereby incorporated by reference in its entirety. The EPRY method is based on images acquired using coherent illumination, such as from light-emitting diodes (LEDs) placed sufficiently far away from the sample or a collimated laser beam, to provide coherent illumination with a consistent beam profile to the sample at varied illumination angles sequentially (i.e. at different sample times). The EPRY method uses the sequence of images captured when the sample is illuminated by various angles with coherent illumination to reconstruct the system's aberration function, also known as the pupil function, while simultaneously reconstructing the sample's complex function. However, it is difficult to deliver a consistent illumination beam at varied illumination angles to a sample if the path between the coherent illumination source and the sample is under the influence of unknown refraction effects. For example, if one were to image the retinal surface of a human eye in-vivo, the coherent illumination needs to be provided via the cornea, lens, and the vitreous humor inside the eye before reaching the retinal surface. Because it is very hard to know the exact refractive error caused by these elements, the illumination profile reaching the retinal surface is not usually known and the EPRY technique cannot usually be applied directly to reconstruct the pupil function of the eye without some error introduced. In another example, EPRY cannot usually be applied directly to characterize the aberrations of a digital camera when taking pictures of natural scenes because it is not practical to deliver coherent illumination at varied angles to natural scenes being imaged.

B. Pupil Ptychography Techniques

Generally speaking, pupil ptychography techniques capture a plurality of limited-aperture images and a full aperture image of a sample of interest that is illuminated by monochromatic, spatially-incoherent illumination, computationally determine the aberration of the optical system, and deconvolve the full aperture image to remove the aberration. In the case of a moving sample, unmodulated images are also captured in parallel with the limited-aperture images to be able to correct for the sample's motion. When used to image a wide field-of-view, the aberration of the optical system and, by extension, the pupil function can be expected to show spatial variations and the aberration may not be the same for different regions within the field-of-view. In this case, the entire field-of view of each of the captured images is segmented into smaller tiles (also referred to herein as “tile images”). Within each tile, the aberration can be assumed to be constant and the aberration characterization procedure is applied to each tile. The pupil ptychography techniques use either one of the limited-aperture images, or a slightly expanded limited aperture image, as ground-truth. The ground truth image is then used to deconvolve all the limited-aperture images to recover a point-spread function (PSF) associated with each limited aperture. These PSFs of the limited aperture images are the intensity information of the various low-pass filtered versions of the actual complex PSF of the system with the full aperture opened. The pupil ptychography techniques use a phase retrieval process to synthesize these low-pass PSFs into the full-sized complex pupil function. An example of a phase retrieval process that can be used is described with respect to the flowchart shown in FIG. 6. After reconstructing the complex pupil function, the PSF associated with the complex pupil function can be easily calculated, which can then be used to deconvolve from the full-aperture image to obtain an aberration-removed image of the sample of interest. Because deconvolution can be sensitive to noise and suffer from the PSFs having zeros inside their passband, a robust deconvolution process can be used and/or multiple images taken to reduce the artifacts resulting from deconvolution according to certain implementations.

In certain implementations, an optical system includes one or more optical elements in the optical path between the sample being imaged and the imaging sensor of the imager. In some cases, the optical system includes an aperture modulator. In certain implementations, the imaging methods determine an aberration in the optical system. According to one aspect, the portions of the eye between the retina being imaged and the outer surface of the first lens are considered part of the optical system when determining the aberration.

Certain examples herein pertain to pupil ptychography techniques that can be used to characterize aberration of an optical system using monochromatic, spatially-incoherent illumination from the sample. In some cases, these pupil ptychography techniques can use the reconstructed aberration to deconvolve from an image captured with the optical system to remove the aberration to generate an image (e.g., a fluorescence image) that is aberration-free or substantially free of aberration. Pupil ptychography techniques can be implemented, for example, in retinal imaging or imaging of natural scenes.

In various implementations, a pupil ptychography imaging system includes an aperture modulator, one or more optical components, and at least one imager. In implementations with a non-moving sample, the pupil ptychography imaging system includes an aperture modulator, optical components, and an imager configured to acquire a sequence of N limited-aperture images of a sample being imaged, a full aperture image of the sample with the entire pupil region open, and optionally a slightly larger than limited-aperture image i.e. one based on a slightly larger pupil region than the limited aperture images. If the sample is moving, a second imager (with unmodulated pupil i.e. full aperture) is implemented to keep track of the motion of the sample. In implementations with a moving sample, the pupil ptychography imaging system includes an aperture modulator, optical components, a first imager, and a second imager. The first imager is configured to acquire a sequence of N limited-aperture images of the moving sample, a full aperture image of the sample with the entire pupil region open, and optionally a slightly larger than limited-aperture image i.e. one based on a slightly larger pupil region than the limited aperture images. The second imager is configured to acquire unmodulated images of the moving sample in parallel with the first imager capturing images of the sample to account for relative movement of the sample for any of the images that the first imager is acquiring.

In certain implementations of systems described herein, a light source (also referred to as an “illumination source”) illuminates the sample being imaged. In some cases, the light source is an incoherent light source. In other cases, the light source is a coherent source with some finite coherence length. The field incident on the sample can be scrambled (e.g. with a long multimode fiber, diffuser, etc.) so that it is spatially incoherent. In a retinal imaging implementation, for example, an illumination source is used to illuminate the sample. In other implementations, such as an implementation for imaging natural scenes, illumination is provided by ambient light and/or by a separate light source. The one or more optical components of a pupil ptychography system are configured to propagate light reflected from the sample to the aperture modulator, and from the aperture modulator to the first imager. In the case of a moving sample, the optical components also propagate light from the sample directly to a second imager.

In the case of a non-moving sample implementation, the first imager and the aperture modulator are synced (synchronized) so that the first imager captures one of a sequence of N limited-aperture images at the same time as the aperture modulator provides an aperture at one of the N different locations at the Fourier plane of the first imager. The same procedure applies to the full aperture and slightly-bigger-limited-aperture images, with the first imager synchronized to capture an image when the aperture modulator, e.g., a spatial light modulator (also referred to herein as “SLM”), displays the associated aperture. In the case of a moving sample implementation, the first imager, the second imager, and the aperture modulator are synced so that the first imager capture a limited aperture image and the second imager capture an unmodulated image at the same time as the aperture modulator provides an aperture at one of the N different locations at the Fourier plane of the first imager. For example, the aperture modulator may be an SLM that displays an aperture on the first imager's Fourier plane for each image capture. Depending on the optical system being measured, these intensity measurements taken by the imager(s) can have long durations or performed quickly for cases such as retinal imaging of an in-vivo eye. In the case of retinal imaging of an in-vivo eye or other moving samples, the images captured at different sample times may have relative spatial shifts with respect to one another due to the sample's movement. These shifts can be correctly registered by using the second imager's images since these images are not modulated in any way other than by the movement. This motion registration is an important operation implemented prior to characterizing the aberration of the optical system since the lateral shift in the captured images may incorrectly encode aberration information in the reconstruction process. The pupil ptychography imaging system also includes one or more processors for executing instructions for implementing the pupil ptychography imaging method described with respect to FIGS. 5 and 6 to reconstruct the pupil function of the optical system and an aberration-removed image of the surface of interest.

Some embodiments of the pupil ptychography methods and systems may provide one or more technical advantages. For example, certain embodiments can correct for the optical distortions of the eye or a poor camera lens (since images of natural scenes are generally taken with cameras) image acquisition which provides a simpler (simpler to use and simpler optics) and less expensive scheme than conventional methods. In addition, pupil ptychography methods and systems use spatially incoherent illumination, which is immune to speckle noise. In addition, since the pupil ptychography methods and systems perform aberration correction post-acquisition, the pupil ptychography method is robust since the aberration correction process and image acquisition process are separated. Aberration correction can be done and the image rendering can be finessed at a later time after image acquisition, without imposing additional time during the acquisition process. One advantage to pupil ptychography techniques is that aberration correction can be done after image acquisition. This can be an advantage over conventional retinal imaging, for example, which require that aberration be corrected during image acquisition which extends examination time which could become uncomfortable for a patient. Also, certain embodiments of the pupil ptychography methods and systems can be used to refocus the corrected image after image acquisition, which also allows for the ability to generate a topological profile of the sample. The refocusing can be done digitally by deconvolving the captured full-aperture sample image with the associated defocus and finding the plane with the sharpest contrast in the image. The location of such plane represents the topological height of that region; doing this for multiple regions in the retina can generate the topological map of the retina.

B. Pupil Ptychography Imaging Systems

FIG. 1 illustrates a simplified block diagram of a pupil ptychography imaging system 10, according to various implementations. The pupil ptychography imaging system 10 includes a computing device 20 with one or more processors 22 and an internal memory 24 in electrical communication with the one or more processors 22. The pupil ptychography imaging system 10 further includes an aperture modulator 32, optical components 34, and at least one imager 36. In implementations with a non-moving sample, the pupil ptychography imaging system 10 implements a first imager. In implementations with a moving sample, the pupil ptychography imaging system 10 further implements a second imager for tracking motion of the moving sample. As denoted by solid lines between the illustrated optical components 34, the optical components 34 are configured to propagate light reflected from the sample being imaged to the aperture modulator 32 and from the aperture modulator 32 to a first imager of the imagers 36. In an implementation for a moving sample, the optical components 34 are further configured to propagate light reflected from the sample to a second imager of the imagers 36. The second imager is configured to acquire unmodulated images of the moving sample in parallel with the first imager capturing images of the sample to account for relative movement of the sample for any of the images that the first imager is acquiring.

The pupil ptychography imaging 10 further includes a communication interface 52 and a display 50 in communication with the communication interface 52. The computing device 20 is configured or configurable to output raw data, processed data such as image data, and/or other data over the communication interface 52 for display on the display 50. Optionally (denoted by dashed lines), the pupil ptychography imaging 10 may further comprise one or more of a communication interface 62 and an external computing device 60 in communication with the communication interface 62, a communication interface 72 and an external memory device 70 in communication with the communication interface 72 for optional storage of data to the external memory device 70, and a communication interface 82 in communication with a user interface 80 for receiving input from an operator of the system 10. The optional user interface 80 is in electrical communication with the computing device 20 through the communication interface 82 to be able to send a control signal to the computing device 20 based on input received at the user interface.

In certain implementations, an imaging system (pupil ptychography system or CACAO-FP system) includes an aperture modulator, which is a device that can pass (or reflect) light selectively through (or from) one or more regions at a plane. An example of a suitable aperture modulator is a spatial light modulator (also referred herein to an “SLM) that can selectively block/reflect light or transmit light from one or more aperture region(s). An example of a commercially-available spatial light modulator is the reflective HOLOEYE® spatial light modulator sold by Pluto, which is a phase only liquid-crystal-on-silicon (LCoS) spatial light modulator with 8 μm pixel size and a 1080×1920 pixels display. Another example of a commercially-available spatial light modulator is the ferroelectric liquid-crystal-on-silicon (LCOS) SXGA3DM-HB made by 4DD®. Another example of a suitable aperture modulator is a digital micromirror device. An example of a suitable commercially-available digital micromirror device is the DLP9000/DLP9000X DLP® device by Texas Instruments®. In various embodiments, the aperture modulator is configured to generate transmissive or reflective apertures (in some cases with different sizes) at different times at various locations along a surface at the Fourier (pupil) plane of the imager. For example, a first aperture may be located at a position x₁, y₁ at time t₁ and a second aperture may be located at a position x₂, y₂ at time t₂. The locations of the modulated apertures and the exposure times of the first imager can be synchronized so that the first imager can take a plurality of limited aperture images based on the different locations of the modulated apertures at the Fourier plane. For example, the aperture modulator may modulate an aperture with a first size at a first location during the exposure time needed to capture a first, limited aperture image, and then modulate an aperture with the first size at a second location during the exposure time needed to capture a second, limited aperture image, and so on until a plurality of limited aperture images based on apertures having the first size has been captured. The aperture modulator can also modulate an aperture equivalent to the desired system numerical aperture (NA) during an exposure time needed to capture a full aperture image.

In FIG. 1, the aperture modulator 32 is configured to modulate apertures having a first size sequentially to N different locations at a surface placed at the Fourier plane of the first imager of the imagers 36. While the apertures having the first size are modulated sequentially to N different locations, the first imager acquires a sequence of N limited-aperture images (i.e. limited by the aperture of the first size) of the sample. Optionally, the aperture modulator 32 may also be configured to modulate an aperture of a second size to the surface at the Fourier plane of the first imager of the imagers 36 at another sample time. In this implementation, while the aperture having the second size is modulated to the Fourier plane, the first imager acquires a limited aperture image based on the second size. Some examples of a first size of an aperture that may be used include 10%, 20%, and 30% of the optical system's numerical aperture (NA). The second size may be larger than the first size, for example, at least 5% larger, at least 10% larger or at least 15% larger.

According to various implementations, a pupil ptychography imaging system includes at least one imager configured to be activated during various exposure (sample) times to capture images of the sample during an image acquisition cycle. In implementations with a moving sample, the pupil ptychography imaging system implements a first imager and a second imager for tracking motion. The pupil ptychography imaging system 10 shown in FIG. 1 includes a first imager for capturing limited aperture images and a full aperture image. Optionally, the pupil ptychography imaging system 10 may further implement a second imager for capturing unmodulated images used to track relative motion of the sample. In one implementation, the pupil ptychography imaging system 10 may comprise both the first imager and second imager and then only use the unmodulated images taken by the second imager for motion correction or may only capture unmodulated images by the second imager if it is determined that that the sample is moving.

The limited aperture images captured by the first imager are based on apertures modulated at a surface at the Fourier plane of the first imager by the aperture modulator 32. The first imager is generally configured to capture a sequence of N limited-aperture images (also referred herein as “a series of N limited-aperture images”) and a full aperture image. The second imager is generally configured to capture a series of unmodulated-aperture images in parallel with the first imager for the correction of the sample's motion.

As used herein, a “limited aperture image” refers to an image acquired based on a limited pupil function, which is a portion of the full pupil function of the optical system. The limited pupil function is defined by the aperture size at the Fourier plane as modulated by the aperture modulator. The size of an aperture at the Fourier plane corresponds to a spatial frequency range of the complex image and the pupil function being captured. The image data of each limited aperture image includes intensity information of the full aperture image, low-pass filtered by the restricted region of the full pupil function.

As used herein, a “full aperture image” (also sometimes referred to herein as a “full pupil image”) refers to an image acquired based on the full pupil function. The full aperture image is captured while the aperture modulator displays an aperture equivalent to the desired system numerical aperture.

As used herein, an “unmodulated image” refers to an image that is not modulated by the aperture modulator. For example, an image acquired by the second imager of the pupil ptychography system in FIG. 3 is not modulated by an aperture modulator and is only modulated by spatial shifts of the moving sample. In this example, the parallel sequence of unmodulated-aperture images is used for image registration of first imager's images for motion correction.

In one implementation, the first imager of a pupil ptychography is configured to capture limited-aperture images based on different apertures sizes. For example, the first imager of a pupil ptychography system may capture a sequence of N limited-aperture images based on a first aperture size, capture a slightly larger limited-aperture image based on a second aperture size that is slightly larger than the first aperture size, and capture a full aperture image. The slightly larger limited-aperture image has a slightly larger frequency range. For example, the second aperture may have an aperture size that is one of 5%, 10%, or 15% larger than the first aperture size.

During a general operation of the pupil ptychography imaging system 10, a sample being imaged is illuminated by monochromatic, spatially-incoherent light. Light reflected from the surface(s) of the sample is collected to the aperture modulator 32 by the optical components 34. If the sample is moving, the pupil ptychography imaging system 10 has a second imager and the optical components 34 are further configured to propagate light reflected from the surface(s) of the sample to the second imager of the imagers 36. During an image acquisition cycle, the computing device 20 sends one or more signals to the aperture modulator 32 and the first imager to synchronize the exposure times for capturing the sequence of N limited aperture images with the aperture modulator 32 modulating apertures (also called windows) at N different locations at the Fourier plane of the first imager. The computing device 20 also sends one or more signals to the aperture modulator 32 and the first imager to synchronize the exposure time for capturing a full aperture image while the aperture modulator 32 displays an aperture equivalent to the desired system NA. The desired system NA may be determined by the maximum, or close to the maximum NA of the optical system. This is defined by the f number in the case of a camera lens, and by the focal length and the pupil size of the eye in the case of an in vivo eye. In one implementation for imaging a moving sample, the computing device 20 also sends one or more signals to the second imager to synchronize the exposure times with the first imager so that the second imager captures unmodulated images of the sample for motion registration. Optionally, the aperture modulator 32 also modulates a second aperture at the Fourier plane of a first imager where the second aperture is larger than the first aperture and the first imager captures a limited aperture image based on the larger aperture size. The processor(s) 22 receives one or more signals with the image data from the images captured by the imager(s) 36. The processor(s) 22 executes instructions to perform functions of the pupil ptychography imaging method. In some cases, such as for wide field-of-view imaging, the processor(s) 22 performs a tiling procedure which segments the field-of view of the captured images into smaller tiles (also referred to herein as “tile images”) within which the aberration is assumed to be constant. The processor(s) 22 recovers the pupil function of the optical system given the spatially incoherent images in an aberration characterization procedure. For a wide field-of-view, this procedure recovers a pupil function for each tile region. During the aberration characterization procedure, a phase retrieval process is used to synthesize the intensity information of the low-passed point spread functions (PSFs) of the N limited aperture images into a full-sized complex pupil function of the optical system. The point spread function of the optical system can be calculated from the complex pupil function. In a deconvolving procedure, the processor(s) 22 deconvolve the full aperture image to generate a substantially aberration free or aberration free complex image (e.g., a fluorescence image) of the sample. For a wide field-of-view image, the deconvolving procedure deconvolves each of the tile images to generate aberration-free or substantially aberration free tile images and then combines (mosaics) together the images to form a full field of view image.

Generally, pupil ptychography imaging systems described herein are configured to acquire a sequence of N limited-aperture images of a sample, a full aperture image with the entire pupil region open, and optionally an image with a slightly larger aperture than the N limited-aperture images. In the case of a moving sample, the pupil ptychography imaging system is further configured to acquire a parallel sequence unmodulated-pupil images. Each pupil ptychography imaging system includes an aperture modulator, optical components, and at least one imager. In some cases, the pupil ptychography imaging systems also include an illumination source which provides monochromatic, spatially-incoherent illumination to the surface of the sample being imaged. In other cases, such as an implementation used to image natural scenes, incoherent illumination can be provided by ambient sunlight or an illumination source separate from the system.

In one aspect, an illumination source is configured to provide monochromatic, spatially-incoherent illumination to the surface of a sample being imaged. An example of such a monochromatic, spatially-incoherent illumination source includes a diffuse laser emitting diode (LED) or a superluminescent diode (SLD). In one particular implementation, the illumination source includes one or more extended LEDs or SLDs coupled to a multimode optical fiber for directing the illumination to the sample being imaged. The LED/SLD is also in electrical communication with a power source or in electrical communication with a computing device that controls power to the LED/SLD. The LED/SLD may be triggered to be switched on only for the duration of the camera's exposure window to reduce the sample's exposure to light. As an example, a fiber coupled LED (e.g. M530F2 from Thorlabs) with an LED driver (DC2200 from Thorlabs) allow for externally triggered illumination. In another aspect, an illumination source is configured to generate monochromatic, coherent illumination and the refractive entities between the illumination source and the surface of interest make the illumination to the surface incoherent. For example, a laser diode coupled to a long multimode fiber can provide a spatially incoherent light provided that the different optical modes in the fiber are sufficiently temporally separated to reduce the temporal coherence. In another implementation, the illumination source is a broadband light source, such as a mercury lamp or the sun, with a bandpass filter HO nm bandpass region).

According to various implementations, a pupil ptychography imaging system includes an aperture modulator which modulates apertures to N different locations at a surface located at the Fourier plane of an imager. In one case, the aperture modulator is configured to shift the transmissive (reflective) aperture(s) to N different locations in 1 second. In another case, the aperture modulator is configured to shift the transmissive (reflective) aperture(s) to N different locations in 0.5 seconds. In another case, the aperture modulator is configured to shift the transmissive (reflective) aperture(s) to N different locations in 0.1 seconds.

According to various implementations, a pupil ptychography imaging system includes a first imager that acquires a sequence of N limited aperture images. In some implementations, N is in a range of 30-60. In another implementation, N is in a range of about 100-200. Generally the more severe the aberration, the higher the number N of limited aperture images would be used. According to moving sample implementations, a pupil ptychography imaging system includes a second imager that acquires, in parallel (i.e. during image acquisition cycle), unmodulated images.

In certain implementations of imaging systems, the aperture modulator is in the form of an SLM that be digitally addressed to quickly shift a transmissive (reflective) aperture(s) across its display. A commercially-available example of an SLM is the LC-R 720 made by HOLOEYE®. In implementations where the aperture modulator is an SLM, N is the number of total shifted SLM admittance functions. Generally an SLM includes an SLM display with discrete display elements. Each discrete SLM element can be set to function as an aperture (aperture setting) or to function as the area surrounding the aperture (field setting). In some aspects, an SLM display element in an aperture setting is transparent or nearly transparent to pass incident light and a display element in a field setting may block/reflect or nearly bock/reflect incident light. In other aspects, certain SLM display elements may be reflective. In these cases, a display element in the aperture setting is oriented at a (first) angle to reflect incident light to the next optical element in the optical arrangement and a display element in a field setting is oriented at a different (second) angle that reflects incident light away from the next optical element. In these aspects, the SLM display can generate an aperture at one or more SLM display elements by setting these display elements in an aperture setting and/or setting the surrounding display elements in a field setting. At different image acquisition times, t_(i), different sets of one or more display elements are at appropriate settings to generate the aperture at the corresponding aperture location. In one case, the SLM display may have a refresh rate in the range of 30 per second to 100 per second. In another case, the SLM display may have a refresh rate in the range of 100 per second to 200 per second.

In certain implementations of imaging systems, the aperture modulator is the form of an LCoS display. The LCoS display is a reflective display having a plurality of reflective display elements. An example of a commercially-available LCoS display is the reflective SLM, Pluto, phase-only LCoS, 8 μm pixel size, 1080×1920 pixels display by HOLOEYE®.

In certain implementations of imaging systems, the aperture modulator is the form of a digital micromirror device. The digital micromirror device includes an optical semiconductor chip having on its surface multiple microscopic micromirrors. In certain aspects, each micromirror can be individually rotated to an angle, α. In this way, each micromirror can be transitioned to either an aperture setting at angle, α, or to a field setting at no rotation, or vice versa. Although these micromirrors are usually arranged in a rectangular array (dimensions o×p), other arrangements may be used. In certain aspects, each micromirror of the digital micromirror device may correspond to one or more light detector pixels. In one case, one or more of the micromirrors in the aperture setting may be oriented so that an optical axis orthogonal to the surface of the micromirror is oriented at an angle, α, from the Fourier plane.

An imager of a pupil ptychography imaging system generally includes at least one image sensor configured to detect light and output a data signal with image data of the intensity distribution (also referred to herein as a “light intensity distribution,” or simply as an “image”) over the sensing surface of the image sensor. The image data output from an image sensor is transmitted (or “sent” or “communicated”) in a signal to image sensor(s) to one or more processors. The image sensor(s) acquire an image by measuring an intensity distribution of light incident its sensing area during an exposure time. Some examples of suitable image sensors are CMOS sensors, a charge-coupled device (CCD), and other similar devices. In one embodiment, an image sensor is a CMOS having a pixel size 11 μm such as the pco dimax HS4. In certain implementations, each image sensor of the first imager and/or second imager is a monochromic light detector. In some cases, one of the imagers of the system may be capable of high-speed capturing of a sequence of images, which may be particularly useful in retinal imaging, for example. In one case, an imager may be configured to acquire images at about 200 frames/second. In one case, an imager may be configured to acquire images at about 100 frames/second. In one case, an imager may be configured to acquire images at about 500 frames/second. An example of an imager capable of high-speed capturing is a high-speed digital camera such as, for example, the 340M-CL Fast Frame Rate CCD Camera made by Thorlabs®.

In certain implementations such as the examples shown in FIGS. 3 and 4, the pupil ptychography imaging system includes as first imager and a second imager. The image sensor(s) of the first imager are configured to acquire limited-aperture images and a full aperture image of the sample, and the second imager is configured to acquire an unmodulated image of the sample during an image acquisition cycle. Optionally, the image sensor(s) of the first imager are configured to acquire a sequence of N limited-aperture images based on a first aperture size and capture a limited aperture image of the aperture based on a second aperture size that is larger than the first aperture size.

According to various embodiments, the pupil ptychography imaging system includes optical components (e.g., beam splitters, objective lenses and/or other lenses, etc.) configured to propagate light reflected from the sample to the aperture modulator, from the aperture modulator to a first imager. Optionally, the optical components may also propagate light reflected from the sample to a second imager. In some cases, the optical components may be in a 4f or 6f arrangement that will allow for the modulation of the spatial spectrum using an aperture modulator that modulates aperture(s) at the Fourier plane of an imager. Examples of optical components are described with respect to FIGS. 3 and 4.

The one or more processor(s) 22 of the computing device 20 and, additionally or alternatively, other processor(s) of the pupil ptychography imaging system 10 (e.g., a processor of the external computing system 60) execute instructions stored on a computer readable memory (e.g., the internal memory 24 or external memory 70) to perform operations of the pupil ptychography imaging system 10. For example, the one or more processor(s) 22 of the computing device 20 may send control signals to the aperture modulator 32 to modulate apertures at different locations and may send control signals to the imager(s) 36 to activate exposure times to take intensity measurements to capture images during image acquisition. The one or more processor(s) 22 of the computing system 20 may also perform operations of the pupil ptychography imaging method to process the intensity measurements to determine the aberration of the optical system and an aberration-free image of the sample. An example of pupil ptychography imaging method is described with respect to FIG. 5. FIG. 6 illustrates an example of a phase retrieval procedure that can be used by the pupil ptychography imaging method in FIG. 5.

According to certain implementations, the computing device of a pupil ptychography imaging system can perform parallel image processing. To perform parallel image processing, the computing device generally includes at least one processor (or “processing unit”). Examples of processors include, for example, one or more of a general purpose processor (CPU), an application-specific integrated circuit, an programmable logic device (PLD) such as a field-programmable gate array (FPGA), or a System-on-Chip (SoC) that includes one or more of a CPU, application-specific integrated circuit, PLD as well as a memory and various interfaces. In some cases, the computing device is in communication with at least one internal memory device. The internal memory device can include a non-volatile memory array for storing processor-executable code (or “instructions”) that is retrieved by the processor to perform various functions or operations described herein for carrying out various logic or other operations on the image data. The internal memory device also can store raw and/or processed image data (including acquired images and aberration free images). In some implementations, the internal memory device or a separate memory device can additionally or alternatively include a volatile memory array for temporarily storing code to be executed as well as image data to be processed, stored, or displayed. In some implementations, the computing device itself can include volatile and in some instances also non-volatile memory.

Each of the communication interfaces 52, 62, 72, and 82 is in electrical communication with the computing device 20. The described electrical communication between components of the pupil ptychography imaging system 10 may be able to provide power and/or communicate data. The electrical communication between components of the pupil ptychography imaging system 10 described herein may be in wired form and/or wireless form.

In FIG. 1, the computing device 20 is in communication with the communication interface 52 which is in communication with the display 50. In certain implementations, the computing device 20 is configured or configurable by a user (also referred to herein as an “operator”) to output raw data or processed data over the communication interface 52 for display on the display 50. In some implementations, the computing device 20 also can be configured or configurable to output raw data as well as processed data (for example, after image processing) over a communication interface 62 to an external computing system 60. Indeed, in some implementations, one or more of the pupil ptychography imaging operations can be performed by such an external computing system 60. In some implementations, the computing device 20 also can be configured or configurable by a user to output raw data as well as processed data over a communication interface 72 for storage in an external memory device 70.

In some implementations, the pupil ptychography imaging system 10 further includes one or more additional interfaces such as, for example, various Universal Serial Bus (USB) interfaces or other communication interfaces. Such additional interfaces can be used, for example, to connect various peripherals and input/output (I/O) devices such as a wired keyboard or mouse or to connect a dongle for use in wirelessly connecting various wireless-enabled peripherals. Such additional interfaces also can include serial interfaces such as, for example, an interface to connect to a ribbon cable. It should also be appreciated that the various system components can be electrically coupled to communicate with the computing device 20 over one or more of a variety of suitable interfaces and cables such as, for example, USB interfaces and cables, ribbon cables, Ethernet cables, among other suitable interfaces and cables.

The data signals output by the image sensors may in some implementations be multiplexed, serialized or otherwise combined by a multiplexer, serializer or other electrical component of the imaging system before being communicated to the computing device. In certain implementations, the computing device can further include a demultiplexer, deserializer or other device or component for separating the image data from each of the image sensors so that the image frames can be processed in parallel by the controller.

Some examples of pupil ptychography imaging systems are shown in FIGS. 2, 3, and 4. Some of these pupil ptychography imaging systems have one or more components that are similar to those described with respect to pupil ptychography imaging system 10 in FIG. 1.

Example of Retinal Imaging Configuration

FIG. 2 is a schematic diagram of components of a pupil ptychography imaging system 200 implemented for retinal imaging, according to embodiments. The illustrated pupil ptychography imaging system is configured for imaging a retinal surface of a moving in-vivo eye. At a high level, the pupil ptychography imaging system 200 is configured to illuminate the retina of an eye with monochromatic, spatially-incoherent illumination, capture a sequence of N limited-aperture retinal images during an image acquisition process, capture a full pupil image, capture unmodulated retinal images during an image acquisition process, determine the pupil function of the optical system based on the image data, and correct the full pupil image to generate a substantially aberration-free or aberration-free complex image of the retina. The optical system in this implementation includes the portion of the eye to the retina. For illustration purposes, pupil ptychography imaging system 200 is shown with a person 201 positioned during the image acquisition process.

The pupil ptychography imaging system 200 includes a casing 210 that contains components of the pupil ptychography imaging system 200 including, for example, an illumination source, optical components, an aperture modulator, and a first and second imager. The casing 210 has a transparent region 212 for allowing light from the illumination source inside the casing 210 to illuminate the retina of the eye of the person 201. For simplicity, the casing 210 is shown here in the shape of a cylinder and the transparent region 212 is circular. Other shapes can be used. The transparent region 212 may be an aperture filled with a transparent material or may be an open aperture. The pupil ptychography imaging system 200 is also shown with an optional chin rest 220 for positioning the person 201 and their eye at a certain distance from the collection optics inside the casing 210. The optional chin rest 220 can also help stabilize or prevent movement of the person 201 during the image acquisition process. The casing 210 may be mounted to the wall or placed on or mounted to a platform such as a desk, a stand, or a chair for receiving the person 201. The chin rest 220 may be mounted to the same object as the casing 210 or another object.

The pupil ptychography imaging system 200 also includes a computing device 230 having one or more processors and a computer readable medium (CRM), e.g., memory, in electronic communication with the one or more processors. The one or more processors execute instructions stored on the CRM to complete operations of a pupil ptychography imaging method. The pupil ptychography imaging system 200 also includes a display 240 and one or more input devices 250 (e.g., keyboard and mouse), both of which are in electronic communication with the computing device 230. The components of the pupil ptychography imaging system 200 inside the casing 210 are in electronic communication with the computing device 230 via wiring. Although many of the components of the pupil ptychography imaging system 200 are shown in electronic communication with each via wiring, it would be understood that the electronic communication between components of pupil ptychography imaging systems described herein can be in wired form, wireless form, or a combination thereof.

According to various embodiments, output from operations of the pupil ptychography imaging method such as an aberration-free or substantially aberration-free image of the retina can be displayed on a display such as the display 240 shown in FIG. 2. In FIG. 2, the one or more processors of the computing device 230 execute instructions stored on the CRM to generate display data that is transmitted in a signal to the display 240.

FIG. 3 is a schematic diagram of components of a pupil ptychography imaging system 300 implemented for retinal imaging, according to embodiments. The illustrated pupil ptychography imaging system is configured for imaging a retinal surface of a moving in-vivo eye. In one example, the components of pupil ptychography imaging system 300 may be an example of components that are contained in the casing of the system 200 shown in FIG. 2.

In FIG. 3, the pupil ptychography imaging system 300 includes an illumination source 310, various optical components, a first imager 350 (e.g., high speed digital camera) for acquiring limited-aperture images and a full aperture image, a second imager 351 (e.g., high speed digital camera) for acquiring unmodulated image(s), and an aperture modulator 360 (e.g. spatial light modulator) for modulating apertures at the Fourier plane of the first imager 350. The pupil ptychography imaging system 300 is shown at an instant in time when the illumination source 310 is providing monochromatic, spatially-incoherent illumination 312 to the retinal surface 321 of the eye 320. The pupil ptychography imaging system 300 also includes various optical components that are configured to propagate light reflected from the retinal surface 321 and passing out the eye 320 to the second imager 351 and to the aperture modulator 360. The optical components are also configured to propagate light from the aperture modulator 360 to the first imager 350.

In FIG. 3, the illumination source 310 includes an extended diffuse LED or an extended SLD coupled to a first end of a multimode fiber. The extended diffuse LED or extended SLD is designed to generate monochromatic, spatially-incoherent light. The multimode fiber may then be manipulated to point the opposing second end of the multimode fiber to direct monochromatic, spatially-incoherent illumination from the second end. In other implementations, other illumination sources may be used. An extended broadband light source such as a mercury lamp may be bandpass filtered to provide a short bandwidth (˜10 nm), spatially incoherent illumination on the sample.

In FIG. 3, the optical components further comprise a first beam splitter 322, a first lens 324 has a focal length, f₂, a second lens 330 having a focal length, f₃, a second beam splitter 332, and a third lens 336 having a focal length, f₃, and a fourth lens 337 having a focal length, f₄. The optical components shown in FIG. 3 are in a 6f arrangement. The first beam splitter 322 is configured to reflect monochromatic, spatially incoherent light 312 from the illumination source 310 to the eye 320. The light propagates through the eye's media (e.g., cornea, aqueous, lens, and vitreous) and is reflected from the retinal surface 321 at the back of the eye 320. The reflected light from the retinal surface 321 is propagated back through the eye's media and to the first beam splitter 322. The first beam splitter 322 is further configured to transmit the part of the light reflected from the retinal surface 321 that is depolarized. An example of a commercially-available beam splitter that can be used is the polarizing beam splitter: PBS251 from Thorlabs. Some suitable beam splitters are polarizing beam splitters designed to reflect the component of the light with a particular polarization direction (e.g. 0 degrees) while transmitting the component with the perpendicular polarization direction (e.g. 90 degrees). Only the part of light that is reflected by the retina that is depolarized will be able to pass through the beam splitter to be captured by the system. Suitable beam splitters are commercially available. Light from the eye 320 is transmitted through the first beam splitter 322 to the first lens 324 (e.g., objective lens) and to the second lens 330 which collimates the light. The second beam splitter 332 reflects a component of the light propagated from the second lens 330 to the third lens 336, which focuses the light at the second imager 351. The second beam splitter 332 transmits another component of the collimated light from the second lens 320 to the aperture modulator 360 which has a display surface at the Fourier plane of the first imager 350. Light incident the aperture modulator 360 within the admittance circular pupil function is reflected to the second beam splitter 332. The second beam splitter 332 reflects the light from the aperture modulator 360 to the fourth lens 337 which focuses the light to the first imager 350. Optionally, the pupil ptychography imaging system 300 may include an adjustable focusing lens between the first beam splitter 322 and the eye 320. In addition or alternatively, the lens 324 may be translated axially to move the system's focal plane around the eye's retinal plane.

During an exemplary image acquisition process of the pupil ptychography imaging system 300, the eye 320 of the patient is positioned in front of the first beam splitter 322 or the first beam splitter 322 is positioned in front of the eye 320. The illumination source 310 receives a control signal to turn on the monochromatic spatially-incoherent illumination 312. Control signals are sent to the first imager 350, the second imager 351, and the aperture modulator 360 to synchronize image acquisition of the various limited aperture images and full aperture image taken by the first imager 350 and the unmodulated images taken by the second imager 351. The first imager 350 and second imager 350 are generally configured to capture aberrated images emerging from the retinal surface 321 of the eye 320 through the optical system of the eye 320. The second imager 351 captures unmodulated images. In parallel, the first imager 350 captures a sequence of N limited-aperture images with the pupil reduced by the aperture modulator 360 in the Fourier plane of the first imager 350. The second imager 351 also captures a full aperture image with an aperture equivalent to the desired system NA. The first imager 350, the second imager 351, and the aperture modulator 360 are synchronized to capture images at the same time while the aperture modulator 360 displays shifted apertures on the Fourier plane of the first imager 350 for each limited aperture image being captured. During an image acquisition cycle, a sequence of N limited-aperture images is captured by the first imager 350 corresponding to N different aperture locations at the Fourier plane, at least one full pupil image is captured by the first imager, and a sequence of unmodulated images is captured by the second imager 351. In one example, N can be in a range of 30 to 60. In another example, N can be from 100 to 200. Optionally, the first imager 350 may capture N limited-aperture images based on a first aperture size and captures another limited-aperture image based on a second aperture size larger than the first aperture size.

Depending on the optical system being measured by a pupil ptychography imaging system of a particular implementation, the images (also referred to as intensity measurements or intensity distributions) taken by the imager(s) may have different exposure times. In some cases, the measurements may have exposure times with long durations such as when imaging natural scenes, from 10 milliseconds to 10 seconds. In other cases, such as when imaging an in-vivo eye, the measurements are performed quickly such as one image per 1-10 milliseconds. In the retinal imaging case, the images captured in the sequence of N limited aperture images may have relative shifts with respect to one another due to the eye's movement during image acquisition. These images are then processed using the pupil ptychography imaging method such as described with respect to FIG. 5 to reconstruct the pupil function of the optical system and an aberration-removed image of the surface of interest.

According to various implementations, a pupil ptychography imaging system implements one or more processors (internal/external) to interpret and process the image data sampled during an image acquisition cycle to generate processed image data. In some implementations, the processor(s) are configured or configurable to perform operations on the image data of a sequence of intensity images to reconstruct a pupil function of the optical system and corresponding aberration, and remove the aberration from a full pupil image of the sample to generate a substantially aberration-free or aberration-free complex image.

In some implementations, a pupil ptychography imaging system is configured to image a moving sample. In these implementations, the pupil ptychography imaging system includes two imagers (e.g., cameras) that are configured to capture the aberrated image emerging from the retinal surface of the eye through the optical system of the eye, or any other optical system and a surface of interest such as a natural scene imaged through a camera lens. One of the imagers captures unmodulated images. In parallel, the other imager captures modulated images either a full aperture image or images with the pupil reduced by the aperture modulator, e.g., SLM, in the Fourier plane of the other imager. These two imagers are synced to captures images at the same time while the aperture modulator displays a variably shifted aperture on the Fourier plane for each modulated image captured. Depending on the optical system being measured, these measurements can have long durations or they need to be performed quickly for cases such as imaging an in-vivo eye. In such a retinal imaging case, the images captured in a sequence may have relative shifts with respect to one another due to the eye's movement. This shift can be correctly registered by using the full-aperture images since these images are not modulated in any way other than by the eye's movement. These full-aperture images are then processed using the pupil ptychography imaging method as described below with reference to FIG. 5 to reconstruct the pupil function of the optical system and an aberration-removed image of the surface of interest.

Example of Natural Scenes Imaging Configuration

FIG. 4 is a schematic diagram of components of a pupil ptychography imaging system 400 implemented for imaging of a natural scene 422, according to embodiments. The pupil ptychography imaging system 400 includes various optical components, a first imager 450 (e.g., high speed digital camera) for acquiring N limited-aperture images and a full aperture image, a second imager 451 (e.g., high speed digital camera) for acquiring unmodulated images, an aperture modulator 460 (e.g. spatial light modulator) for modulating apertures at the Fourier plane of the first imager 450. The pupil ptychography imaging system 400 is shown at an instant in time when spatially-incoherent illumination 412 is provided to the natural scene 422 being imaged by the system 400. The various optical components are configured to propagate light reflected from the natural scene 422 to the second imager 451, propagate light reflected from the natural scene 422 to the aperture modulator 460, and propagate light from the aperture modulator 460 to the first imager 450. Although not shown, the optical components further include a bandpass filter configured to filter the light reflected from the natural scene. A bandpass filter with a bandwidth of about 10 nm would be suitable.

In FIG. 4, the optical components comprise a first lens 424, a second lens 430, a beam splitter 432, and a third lens 436, and a fourth lens 437. During image acquisition, spatially-incoherent illumination 412 illuminates the surface(s) of interest of the natural scene 422. Flight reflected from the surface(s) propagate to the first lens 424 (e.g., objective lens) and to the second lens 430 which collimates the light. The beam splitter 432 reflects a component of the collimated light from the second lens 420 to the third lens 436, which focuses the light to the second imager 451. The beam splitter 432 transmits another component of the collimated light from the second lens 420 to the aperture modulator 360 which has a display surface at the Fourier plane of the first imager 450. Light incident the aperture modulator 440 within the admittance circular pupil function is reflected to the beam splitter 432. The beam splitter 432 reflects light from the aperture modulator 440 to the fourth lens 437, which focuses light propagated from the beam splitter 432 to the first imager 450.

During an exemplary image acquisition process of the pupil ptychography imaging system 400, one or more control signals are sent by a processor(s) to the first imager 350, the second imager 351, and the aperture modulator 460 to synchronize image acquisition of the various limited aperture images and full aperture image taken by the first imager 450 and the unmodulated images taken by the second imager 451. The first imager 450 and second imager 450 are generally configured to capture aberrated images emerging from the surfaces of the natural scene 422 through the optical system of the natural scene. The second imager 351 captures one or more unmodulated images of the natural scene 422, and in parallel, the first imager 350 captures a sequence of N limited-aperture images of the natural scene 422 with the pupil reduced by the aperture modulator 360 in the Fourier plane of the first imager 450. The second imager 451 also captures a full aperture image of the natural scene 422 with an aperture equivalent to the desired system NA. The first imager 450, the second imager 451, and the aperture modulator 460 are synchronized to capture images at the same time while the aperture modulator 460 displays shifted apertures on the Fourier plane of the first imager 450 for each limited aperture image being captured. During an image acquisition cycle, a sequence of N limited-aperture images of the natural scene 422 is captured by the first imager 450 corresponding to N different aperture locations at the Fourier plane, at least one full pupil image is captured of the natural scene 422 by the first imager, and unmodulated images of the natural scene 422 is captured by the second imager 451. In one example, N can be from 30 to 60. In another example, N can be from 100 to 200. Optionally, the first imager 450 may capture N limited-aperture images based on a first aperture size and captures another limited-aperture image based on a second aperture size larger than the first aperture size.

In various implementations, the second imager captures one or more unmodulated images. In one implementation, the second imager captures N unmodulated images. In another implementation, the second imager captures one unmodulated image. In another implementation, the second imager captures two unmodulated images. In another implementation, the second imager captures less than N unmodulated images.

C. Pupil Ptychography Methods

In various embodiments, pupil ptychography methods capture a sequence of N limited-aperture images and a full aperture image of a sample that is illuminated by monochromatic, spatially-incoherent illumination, computationally determine the aberration of the optical system, and deconvolve the full aperture image to remove the aberration. In embodiments with a moving sample, unmodulated aperture images are also captured in parallel in order to correct for the sample's motion. When used to image a wide field-of-view, the aberration of the optical system and, by extension, the pupil function can be expected to show spatial variations and the aberration may not be the same for different regions within the field-of-view. In some cases, a field-of-view is considered to be wide if larger than 1 degree of visual field. In this case, the entire field-of view of each of the captured images is segmented into smaller tile images and the aberration within each tile is assumed to be constant.

With a moving sample, images may shift spatially between sample times of a sequence of images. In an optional motion registration operation, the shifts in the N limited-aperture images and the full aperture image can be correctly registered using the corresponding unmodulated images since these images not modulated in any way other than by sample movement. Registration is an optional operation implemented prior to characterizing the aberration of the optical system since shifting of the captured images may incorrectly encode aberration information in the reconstruction process.

During aberration characterization, the aberration of the optical system is determined. The pupil ptychography methods use either one of the N limited-aperture images or a slightly expanded limited aperture image as ground-truth. The ground truth image is then used to deconvolve all the limited-aperture images to recover a point-spread function (PSF) associated with each limited aperture. These recovered PSFs are of intensity information of the various low-pass filtered versions of the actual complex PSF of the system with the full aperture opened. The pupil ptychography methods use a phase retrieval process to synthesize these low-pass PSFs into the full-sized complex pupil function. After reconstructing the complex pupil function, the PSF associated with the complex pupil function can calculated, which can then be used to deconvolve from the full-aperture image to obtain an aberration-removed image of the sample.

FIG. 5 depicts a flowchart 500 of operations of a pupil ptychography method, according to various implementations. At operation 510, the pupil ptychography method captures aberrated images of the sample illuminated with monochromatic, spatially-incoherent illumination during each image acquisition cycle. During this cycle, the sample may be continuously illuminated or the sample may be illuminated during the exposure times during each image capture. In implementations with a non-moving sample and with a moving sample, a first sequence of N limited-aperture images of the sample and a full aperture image of the sample is captured. The full-aperture image is the image from which the optical system aberration will be removed. Generally, the N limited aperture image and the full aperture image are captured by a first imager synchronized with an aperture modulator that forms apertures at different locations on the Fourier plane of the first imager. Optionally, the first imager also captures an additional limited-aperture image corresponding to a second aperture size of the aperture modulator that is larger than the first aperture size of the aperture modulator corresponding to the N limited aperture images. In an implementation with a moving sample, a sequence of N unmodulated images is also captured in parallel with the N limited-aperture images. Generally, the N limited-aperture images and the N unmodulated images are captured by the first imager and a second imager respectively, which are synchronized to capture the different sequences of images in parallel. That is, the first imager captures a modulated image during the same exposure time as the second imager captures an unmodulated image.

In one implementation, the pupil ptychography system includes a first imager and a second imager and implements the first imager to take modulated images if the sample is not moving and implements the first imager to take modulated images and the second imager to take unmodulated images in parallel if the sample being imaged is moving. Alternatively, both the first imager to take modulated images and second imager to take unmodulated images and then the method only uses the unmodulated images to correct for motion if the method makes a determination that the sample is moving.

At operation 520, optionally (denoted by dashed line) the pupil ptychography method segments the image data of each of the full field-of-view images captured during operation 510 into a matrix of tile images using one or more processors. In one case, the full field-of-view may be segmented into equivalent portions based on keeping each portion less than a size within which the aberration can be assumed to be constant. For example, the full field-of-view may be segmented to keep the field of view of each tile image within a predetermined size. The predetermined size may be, for example, 1 degree, 2 degrees, or 3 degrees of visual field. In one implementation, operation 520 may be invoked if the method determines that the field-of-view is greater than a threshold size. Some examples of threshold sizes are 1 degree, 2 degrees, or 3 degrees of visual field etc.

In the case a moving sample, the limited-aperture images captured at different sample times may have relative spatial shifts with respect to one another due to the sample's movement. These shifts can be correctly registered by using the unmodulated images since these images are not modulated in any way other than by the movement of the sample. At operation 530, optionally (denoted by dashed line) if the sample is considered to be moving, the pupil ptychography method registers the motion of the sample using the unmodulated images captured during operation 510. To register the motion of the sample, a spatial shift of each one of the sequence of N limited-aperture images is determined by comparing the spatial location of the corresponding unmodulated image taken at the same sample time to the unmodulated image taken at the first sample time. For example, a spatial shift of the 5^(th) limited-aperture image taken at t=t₅ is determined by comparing the location of the 5^(th) unmodulated image at t=t₅ to the location of the first unmodulated image taken at t=t₁ and so on. The pupil ptychography method can then correct each limited-aperture image based on the determined spatial shift.

In one implementation, the pupil ptychography method compares two or more of the unmodulated images to determine whether the sample is moving. If movement exists, then the method proceed with operation 530 to correct the limited-aperture images for motion. In other implementations, the pupil ptychography method may always correct for movement.

At operation 540, the pupil ptychography method uses one or more processors to characterize the aberration of the optical system using image data of the spatially incoherent images collected in operation 510. If each of the captured images were tiled in the optional operation 520, then operation 540 is performed to determine an aberration based on each of the tile regions. FIG. 6 depicts a flowchart that describes details of an example of sub-operations of operation 540.

At operation 550, the pupil ptychography method uses one or more processors to deconvolve the full pupil (full aperture) image captured in operation 510 to correct for the aberration determined in operation 540. If each of the captured images were tiled in the optional operation 520, then operation 550 decolvolves each of the tile images of the full aperture image to correct for aberration in each tile region. Then, the pupil ptychography method mosaics the aberration-free or substantially aberration free tile images together to form a full field-of-view image that is aberration-free or substantially aberration free. In one aspect, the aberration-free or substantially aberration free image is a fluorescence image.

In various implementations, a deconvolution operation is used. A blind deconvolution operation can be used when the pupil function of the system. Non-blind deconvolution is used when you have knowledge of the pupil function. Some examples of non-blind deconvolution techniques that can be used include Tikhonov regularization, Wiener deconvolution, block matching and 3D filtering (BR3D).

FIG. 6 depicts a flowchart 600 of sub-operations of aberration characterization process of a pupil ptychography method, according to an implementation.

At operation 602, the pupil ptychography method deconvolves each of the sequence of N limited-aperture images based on a ground truth image to obtain an incoherent point-spread-function, o_(i)(x, y), for i=1 to N. In one example, the ground truth image is one of the limited-aperture images based on the first aperture size. In another example, the ground truth image is the limited-aperture image based on the second aperture size larger than the first aperture size.

At operation 604, the pupil ptychography method initializes a full-aperture pupil function, P(k_(x),k_(y)), with is inside the passband and 0s outside the passband. The pass band is defined by the full aperture's NA in the Fourier domain.

At operation 606, the pupil ptychography method initializes the counter i=1. The incoherent point-spread-functions, o_(i)(x, y), of the N limited aperture images are the intensity information of the various low-pass filtered versions of the actual complex point spread function of the optical system with the full aperture opened.

At operation 608, the method determines the low-pass filtered version of the full-aperture pupil function, P(k_(x),k_(y)), with a limited aperture, B_(i)(k_(x),k_(y)), that corresponds to the incoherent point-spread-functions, o_(i)(x, y). Then, the low-pass filtered version with a limited aperture, B_(i)(k_(x),k_(y)), is Fourier transformed to obtain the coherent point-spread-function p_(i)(x, y) according to: p_(i)(x, y)=F{B_(i)P}. The incoherent PSF is the absolute squared of the coherent point spread function.

At operation 610, the method replaces the amplitude of p_(i)(x, y) with the square root of the incoherent point-spread-function value, o_(i)(x, y) using: p′_(i)=√{square root over (o_(i))}p_(i)/|p_(i)|.

At operation 612, the method updates the corresponding region of the full-aperture pupil function, P(k_(x),k_(y)), with P_(i). P_(i) is the Fourier transform of p′_(i) according to: P_(i)=F{p′_(i)}.

At operation 614, the pupil ptychography method increments the counter i=i+1.

At operation 616, the pupil ptychography method returns to repeat operations 608, 610, 612, 614 until i is greater than N. If i is greater than Nat operation 610, then the method goes on to operation 618 to determine whether the solution has converged. If it is determined that the solution has not converged at operation 618, the method returns to operation 606 to initialize the counter to i=1. If it is determined that the solution has converged at operation 618, the method has reconstructed the solution for the pupil function P(k_(x),k_(y)) at operation 620. The method determines the aberration for the full-aperture image based on the reconstructed pupil function P(k_(x),k_(y)). If the operational tiling operation was performed on the image, the method determines the aberration for the tile image based on the reconstructed pupil function P(k_(x),k_(y)) for the tile region.

Section II—Coded-Aperture-Based Correction of Aberration Obtained from Fourier Ptychography (CACAO-FP) Systems and Methods

A. Introduction

Imaging a sample with an uneven surface or a thick sample with two-dimensional features present at different depths across the field-of-view can result in parts of the image being in focus while other parts are out of focus. For example, a specimen in clinical cytopathology may contain stained cells present at different depth levels, and require a microscopist to capture multiple images while scanning the specimen through the depth. An example of microscopy that captures multiple images at different depths is described in Evered, A., Dudding, N. “Accuracy and perceptions of virtual microscopy compared with glass slide microscopy in cervical cytology,” Cytopathology 22:82-7 (2011), which is hereby incorporated by reference in its entirety. In such a scenario, multiple images have to be taken at different heights to bring different parts of the sample into focus, which can be time consuming. In another scenario, the region of interest in the sample may be embedded in a transparent medium that causes variations in the refractive index. Since an imaging lens, such as a microscope objective lens, is designed for use with a specific refractive index medium between the object plane and the lens, any refractive index mismatch will cause aberrations in the image. For example, a process called CLARITY is typically used to homogenize the refractive index of a mouse brain specimen to be able to image with light sheet fluorescence microscopy. However, some residual refractive index mismatch exists after the CLARITY process, which may cause aberrations when imaging through a thick layer of the tissue. An example of light sheet fluorescence microscopy can be found in Tomer, R. et al. “Advanced CLARITY for rapid and high-resolution imaging of intact tissues,” Nature protocols (2014), which is hereby incorporated by reference in its entirety. An example of imaging of CLARITY-processed mouse brain specimens is described in Reinig, M. R. et al., “Adaptive optics microscopy enhances image quality in deep layers of CLARITY processed brains of YFP-H mice,” Proceedings Volume 9690, Clinical and Translational Neurophotonics, Neural Imaging and Sensing, and Optogenetics and Optical Manipulation, 969008 (2016), which is hereby incorporated by reference in its entirety. In certain instances, adaptive optics methods can be used to help overcome the issue, but these methods sacrifice the massive parallelism offered by the light sheet microscopy.

Certain implementations pertain to coded-aperture-based correction of aberration obtained from Fourier ptychography (CACAO-FP) methods and systems. These CACAO-FP systems and methods are adapted to correct or compensate for sample-induced aberration, along with aberration in the optical system. In many examples, a CACAO-FP system is configured to capture a plurality of incoherent (e.g., fluorescence) images of a sample of a sample being imaged with coded-apertures (also referred to herein as “large masks”) at its pupil plane, synthesize the spatially varying system- and sample-induced aberration using Fourier ptychography techniques, and remove the aberration using deconvolution to obtain substantially aberration-free images of the sample. In this way, the CACAO-FP system is configured to provide coded-aperture-based correction of aberration obtained from Fourier Ptychography. A substantially aberration-free image refers to an image having less than a predefined degree of system- and sample-induced aberration, e.g., resolution degradation from the theoretical performance defined by the system's numerical aperture (i.e. lambda/(2NA)) of less than 1%, less than 2%, less than 3%, less than 4%, or less than 5%.

A CACAO-FP system includes an aperture modulator that can modulate different apertures at the Fourier plane of the imager so that the imager can capture aperture modulated images. The aperture modulator is configured to modulate one or more of a plurality of limited apertures (also sometimes referred to herein as “small masks”), a plurality of coded apertures (also sometimes referred to herein as “large masks”), and a full aperture. Each coded aperture is a mask corresponding to the full pupil size passing/reflecting light and including one or more regions that block/absorb light to form a pattern. This pattern encodes the pupil function and is used to assist in a latent image recovery by deconvolution. For example, an aperture modulator can generate a coded aperture by modulating a full aperture (e.g., circular region) equivalent to the desired system numerical aperture (NA) and overlaying light blocking regions to pass light through the unblocked regions of the full aperture according to a pattern created by these regions. Some suitable examples of patterns include a crescent shape, a binary pattern, a Hadamard pattern, a gradient pattern, etc. Each limited aperture of the plurality of is a smaller region of the full aperture. In some cases, the limited apertures are overlapping regions (e.g., more than 20% overlap between adjacent regions, more than 25% overlap between adjacent regions, more than 30% overlap between adjacent regions) that when combined cover the full aperture.

During an image acquisition process of various implementations, the CACAO-FP system synchronizes the imager and aperture modulator so that the imager captures images while the aperture modulator modulates apertures. During image acquisition, the aperture modulator generates variably-coded apertures (i.e. apertures based on different patterns) during which a corresponding variably-coded aperture images are acquired. In these cases, each coded aperture image corresponds to one of the plurality of variably-coded apertures being generated. During image acquisition, the aperture modulator also generates a plurality of limited apertures during which the imager captures a corresponding plurality of limited aperture images. In one implementation, during image acquisition, the aperture modulator also generates a full aperture during which the imager captures a full aperture image i.e., the aperture does not have any blocking/absorbing regions. In another implementation, a full aperture image may be generated from the plurality of limited-aperture images. For example, a CACAO-FP system may include an aperture modulator configured to modulate at the Fourier plane: (i) a plurality of variably-coded apertures, (ii) a full aperture corresponding to the pupil function of the desired numerical aperture, (iii) and a plurality of limited apertures of the full aperture. During this implementation, an imager is synchronized to acquire: (i) a plurality of variably-coded aperture images, (ii) a full aperture image, and (iii) and a plurality of limited aperture images, respectively. In another example, a CACAO-FP system may include an aperture modulator configured to modulate at the Fourier plane: (i) a plurality of variably-coded apertures, and (ii) a plurality of limited apertures of the full aperture. During this implementation, an imager is synchronized to acquire: (i) a plurality of variably-coded aperture images, and (ii) a plurality of limited aperture images, respectively.

The ability of a CACAO-FP system to remove system- and sample-induced aberration during image reconstruction, rather than at the time of image capture may be advantageous in providing a faster image acquisition process and additional degrees of freedom to tune aberration correction during post-capture. For instance, in a tuning implementation, during the image reconstruction process, defocus parameters and other parameters used to construct the aberration map can be modified between iterations. In one aspect, the image resulting from a particular iteration may be determined to lack sharpness of features and defocus parameters modified before the next iteration to generate a sharper image. In another aspect, if an image is found to have multiple defocus planes, the image may be retiled between iterations to have a finer tile size.

B. CACAO-FP Systems

Some of the components of the CACAO-FP systems described in Section I may be similar to components of the pupil ptychography systems described in Section II.

FIG. 7 is a simplified block diagram of a CACAO-FP system 700, according to various implementations. Certain system components are optional (denoted by dashed line) and any combination of these components is included according to various implementations. As shown in FIG. 7, the CACAO-FP system 700 includes a computing device 720 with one or more processors 722 and an internal memory 724 in electrical communication with the one or more processors 722. The CACAO-FP system 700 further includes an optical system 730 with an aperture modulator 732 that can modulate light and one or more imagers 749 in communication with the optical system 730 to receive propagated light from the optical system 730 and to acquire images. The CACAO-FP system 700 is shown with a sample 711 being imaged at this instance during operation. It would be understood that a sample need not be present in the CACAO-FP system when the system is not in operation in this example and in other examples described herein. Also, it would be understood that although samples described herein may be illustrated or discussed as being of a particular shape or composition, other samples may be imaged by these systems.

At the instance illustrated in FIG. 7, the sample 711 is providing incoherent light such as, e.g., fluorescence emissions from fluorophores activated by excitation light from a light source. The aperture modulator 732 is configured to modulate to provide a plurality of variably-coded apertures and a plurality of limited apertures that are portions of a full aperture equivalent to the desired system numerical aperture. In one aspect, the aperture modulator 732 is also configured to modulate to provide the full aperture. The aperture modulator 732 is configured to provide the apertures at the pupil plane of the imager 740. The CACAO-FP system 700 synchronizes the aperture modulator 732 with the imager(s) 740 so that the imager(s) captures images while the aperture modulator 732 modulates the apertures, e.g., to capture one image for each aperture. The optical system 730 also includes one or more optical components configured to propagate light transmitted through the sample 711 (in the transmission mode) or reflected from the sample 711 (in the reflection mode) to the aperture modulator 732 and from the aperture modulator 732 to the imager(s) 740.

Some examples of suitable aperture modulators are described in detail in Section I. For example, a suitable aperture modulator is a spatial light modulator that can selectively block/reflect light and transmit light from one or more aperture region(s). An example of a commercially-available spatial light modulator is the reflective HOLOEYE® spatial light modulator sold by Pluto®, which is a phase-only LCoS with 8 μm pixel size and a 1080×1920 pixels display. Another example of a suitable aperture modulator is a digital micromirror device. An example of a suitable commercially-available digital micromirror device is the DLP9000/DLP9000X DLP® Digital micromirror device by Texas Instruments®.

The CACAO-FP system 700 further includes an optional communication interface 752 and an optional display 750 in communication with the communication interface 752. The computing device 720 is configured or configurable to output raw data, processed data such as image data, and/or other data over the communication interface 752 for display on the display 750. The CACAO-FP system 700 also includes an optional communication interface 762 and an optional external computing device 760 in communication with the communication interface 762, an optional communication interface 772 and an optional external memory device 770 in communication with the communication interface 772 for optional storage of data to the external memory device 770, and an optional communication interface 782 in communication with an optional user interface 780 for receiving input from an operator of the CACAO-FP system 700. The user interface 780 is in electrical communication with the computing device 720 through the communication interface 782 to be able to send a control signal to the computing device 720 based on input received at the user interface.

According to one aspect, a CACAO-FP system is configured to capture a plurality of limited-aperture images based on apertures of the same size. According to another aspect, a CACAO-FP system is configured to capture a plurality of limited-aperture images based on different aperture sizes.

During operation of the CACAO-FP system 700, the sample 711 being imaged is illuminated, e.g., by a light source. In one aspect, the CACAO-FP system 700 operates in a transmission mode with the light source and collection optical element configured so that the collection optical element receives light transmitted through the sample being imaged. In another aspect, the CACAO-FP system 700 operates in a reflection mode with the light source and collection optical element configured so that the collection optical element receives light reflected from the sample being imaged.

Returning to FIG. 7, light from the illuminated sample 711 is received by one or more optical components of the optical system 730, light propagated to the aperture modulator 732 is filtered by the aperture at the aperture modulator 732, and light is propagated to the imager(s) 740. During image acquisition, the computing device 720 sends one or more signals to the aperture modulator 732 and the imager(s) 740 to synchronize exposure times for capturing images with the aperture modulator 732 modulating apertures (also called windows) at the Fourier plane of the imager(s) 740. In one aspect, the aperture modulator 732 modulates to provide: (i) a plurality of variably-coded apertures, (ii) a full aperture corresponding to the pupil function of the desired numerical aperture, and (iii) a plurality of limited apertures of the full aperture and the imager 740, synchronized with the aperture modulator 732, acquires respectively: (i) a plurality of variably-coded aperture images, (ii) a full aperture image, and (iii) a plurality of limited aperture images. In another aspect, during image acquisition, the aperture modulator 732 modulates to provide: (i) a plurality of variably-coded apertures and (ii) a plurality of limited apertures of the full aperture and the imager 740, synchronized with the aperture modulator 732, acquires respectively: (i) a plurality of variably-coded aperture images, and (ii) a plurality of limited aperture images.

The processor(s) 722 receives one or more signals with the image data captured by the imager(s) 36. The processor(s) 722 executes instructions to perform functions of the CACAO-FP system 700 such as described with respect to FIG. 12. The processor(s) 722 performs a tiling procedure, which segments captured images of the entire field-of-view into tile images within which the aberration is assumed to be constant. The processor(s) 722 recovers the pupil function for each tile image in an aberration characterization procedure. During the aberration characterization procedure, a phase retrieval process is used to synthesize the intensity information of the low-passed point spread functions (PSFs) of the limited aperture images into a full complex pupil function of the optical system. The point spread function of the optical system can be calculated from the complex pupil function. In a deconvolving procedure, the processor(s) 22 deconvolve each of the tile images to generate a substantially aberration free or aberration free tile image.

In various implementations, the sample being imaged by a CACAO-FP system is illuminated by a light source. In one case, the light source is configured to provide monochromatic, spatially incoherent illumination. Some examples of light sources that can provide a monochromatic, spatially-incoherent illumination are a diffuse laser emitting diode (LED) and a superluminescent diode (SLD). In one example, the light source includes one or more extended LEDs or SLDs coupled to a multimode optical fiber for directing the illumination to the sample being imaged. The LED/SLD is also in electrical communication with a power source or in electrical communication with a computing device that controls power to the LED/SLD. The LED/SLD may be triggered to be switched on only for the duration of the camera's exposure window to reduce the sample's exposure to light. As an example, a fiber coupled LED (e.g. M530F2 from Thorlabs) with an LED driver (DC2200 from Thorlabs) allow for externally triggered illumination. In another example, the light source is configured to generate monochromatic, coherent illumination and the refractive entities between the illumination source and the surface of interest make the illumination to the surface incoherent. For example, a laser diode coupled to a long multimode fiber can provide a spatially incoherent light provided that the different optical modes in the fiber are sufficiently temporally separated to reduce the temporal coherence. In another implementation, the light source is a broadband light source, such as a mercury lamp or the sun, with a bandpass filter HO nm bandpass region). In one implementation, the sample plane of interest has fluorescent targets that emit light upon activation by an excitation source such as light or ultrasound, to name a few. Fluorescence from the targets produce the incoherent light to be imaged by a CACAO-FP system.

According to various implementations, a CACAO-FP system includes an aperture modulator which modulates an aperture at different locations at a surface located at the Fourier plane of an imager. In one case, the aperture modulator is configured to modulate to provide apertures at 10 frames per second. In another aspect, the aperture modulator is configured to modulate to provide apertures at 1000 frames per second. In another aspect, the aperture modulator is configured to display multiple apertures per frame.

According to various implementations, a CACAO-FP system includes an imager that acquires one or more of: (i) a plurality of M variably-coded aperture images, (ii) a full aperture image, and (iii) a plurality of N limited aperture images. In one implementation, N is in a range between about 30 and about 60. In another implementation, N is in a range between about 100 and about 200. In another implementation, N is greater than 100. In some cases, the number N is selected based on the severity of the aberration. In one implementation, M is in a range between about 2 and about 10. In another implementation, M is in a range between about 10 and about 20. In another implementation, M is greater than 20. In another implementation, M is greater than 2. In another implementation, M is about 4. In another implementation, M is 1.

In one aspect, the aperture modulator of a CACAO-FP system is a spatial light modulator that can be digitally addressed to generate transmissive or reflective regions on its display to generate a coded aperture, a limited aperture, or a full aperture. A commercially-available example of an SLM is the LC-R 720 made by HOLOEYE®. Generally an SLM includes a display with discrete display elements. Each discrete display element can be set to function as an aperture (aperture setting) that allows light to pass or to function as the light blocking area surrounding the aperture (field setting). For example, a display element in an aperture setting is transparent or nearly transparent to pass light and a display element in a field setting substantially blocks/reflects incident light. At different image acquisition times, t_(i), different sets of one or more display elements are at appropriate settings to generate the desired aperture at the corresponding aperture location. In one aspect, the display may have a refresh rate in the range between about 30 per second and 100 per second. In another aspect, the display may have a refresh rate in the range between about 100 per second and 200 per second.

In one aspect, the aperture modulator of a CACAO-FP system is an LCoS display with reflective display elements. An example of a commercially-available LCoS display is the reflective SLM, Pluto, phase-only LCoS, 8 μm pixel size, 1080×1920 pixels display by HOLOEYE®.

In one aspect, the aperture modulator of a CACAO-FP system is a digital micromirror device. The digital micromirror device includes an optical semiconductor chip having on its surface multiple microscopic micromirrors. In certain aspects, each micromirror can be individually rotated to an angle, α. In this way, each micromirror can be transitioned to either an aperture setting at angle, α, or to a field setting at no rotation, or vice versa. Although these micromirrors are usually arranged in a rectangular array (dimensions o×p), other arrangements may be used. In certain aspects, each micromirror of the DMD may correspond to one or more light detector pixels. In one case, one or more of the micromirrors in the aperture setting may be oriented so that an optical axis orthogonal to the surface of the micromirror is oriented at an angle, α, from the Fourier plane.

In various implementations, a CACAO-FP system includes one or more imagers, each imager with one or more image sensors. Each image sensor is configured to detect light and output a data signal with image data of the intensity distribution (also referred to herein as a “light intensity distribution,” or simply as an “image”) over the sensing surface of the image sensor. The image data output from an image sensor is transmitted (or “sent” or “communicated”) in a signal to image sensor(s) to one or more processors. The image sensor(s) acquire an image by measuring an intensity distribution of light incident its sensing area during an exposure time. Some examples of suitable image sensors are CMOS sensors, a charge-coupled device (CCD), and other similar devices. In one embodiment, an image sensor is a CMOS having a pixel size 11 μm (e.g. an image sensor of the pco.dimax HS4 ® camera available from pco Inc.®). In certain implementations, each image sensor of the first imager is a monochromic light detector. In some cases, an imager may be capable of high-speed capturing of images. In one aspect, an imager can acquire images in a range between about 100 and about 200 frames/second. In one aspect, an imager can acquire images in a range between about 100 and 500 frames/second. In one aspect, an imager can acquire images in a range between about 200 and about 400 frames/second. In one aspect, an imager can acquire images at greater than about 200 frames/second. In one aspect, an imager can acquire images greater at than about 300 frames/second. In one aspect, an imager can acquire images at greater than about 400 frames/second. In one aspect, an imager can acquire images at greater than about 500 frames/second. An example of an imager capable of high-speed capturing is a high-speed digital camera such as, for example, the 340M-CL Fast Frame Rate CCD Camera made by Thorlabs®.

According to various embodiments, a CACAO-FP system includes an optical system with one or more optical components (e.g., beam splitters, objective lenses and/or other lenses, etc.) configured to propagate light reflected from the sample to the aperture modulator and from the aperture modulator to an imager. In some cases, the optical components may be in a 4f or 6f arrangement that allows for the modulation of the spatial spectrum using an aperture modulator that modulates aperture(s) at the Fourier plane of the imager.

The processor(s) 722 of the computing device 720 and, additionally or alternatively, other processor(s) of the CACAO-FP system 700 (e.g., a processor of the external computing system 760) execute instructions stored on a computer readable memory (e.g., the internal memory 724 or external memory 770) to perform operations of the CACAO-FP system 700. For example, the processor(s) 722 of the computing device 720 may send control signals to the aperture modulator 732 to modulate apertures and may send control signals to the imager(s) 736 to activate exposure times to capture images. The one or more processor(s) 720 of the computing system 720 may also perform operations of the CACAO-FP as described in FIG. 8 to determine the aberration of the optical system and sample-induced aberration and generate a substantially aberration-free image of the sample. In one aspect, the aberration-free or substantially aberration free image is a fluorescence image.

According to certain implementations, a CACAO-FP system includes a computing device that can perform parallel image processing. To perform parallel image processing, the computing device generally includes at least one processor (or “processing unit”). Examples of processors include, for example, one or more of a general purpose processor (CPU), an application-specific integrated circuit, an programmable logic device (PLD) such as a field-programmable gate array (FPGA), or a System-on-Chip (SoC) that includes one or more of a CPU, application-specific integrated circuit, PLD as well as a memory and various interfaces. In some cases, the computing device is in communication with at least one internal memory device. The internal memory device can include a non-volatile memory array for storing processor-executable code (or “instructions”) that is retrieved by the processor to perform various functions or operations described herein for carrying out various logic or other operations on the image data. The internal memory device also can store raw and/or processed image data (including acquired images and aberration free images). In some implementations, the internal memory device or a separate memory device can additionally or alternatively include a volatile memory array for temporarily storing code to be executed as well as image data to be processed, stored, or displayed. In some implementations, the computing device itself can include volatile and in some instances also non-volatile memory.

Each of the communication interfaces 752, 762, 772, and 782 is in electrical communication with the computing device 720. The described electrical communication between components of the CACAO-FP system 700 may be able to provide power and/or communicate data. The electrical communication between components of the CACAO-FP system 700 described herein may be in wired form and/or wireless form.

In FIG. 7, the computing device 720 is in communication with the communication interface 752 which is in communication with the display 750. In certain implementations, the computing device 720 is configured or configurable by a user (also referred to herein as an “operator”) to output raw data or processed data over the communication interface 752 for display on the display 750. In some implementations, the computing device 720 also can be configured or configurable to output raw data as well as processed data (for example, after image processing) over a communication interface 762 to an external computing system 760. Indeed, in some implementations, one or more of the CACAO-FP imaging operations can be performed by such an external computing system 760. In some implementations, the computing device 720 also can be configured or configurable by a user to output raw data as well as processed data over a communication interface 720 for storage in an external memory device 770.

In some implementations, the CACAO-FP system 700 further includes one or more additional interfaces such as, for example, various Universal Serial Bus (USB) interfaces or other communication interfaces. Such additional interfaces can be used, for example, to connect various peripherals and input/output (I/O) devices such as a wired keyboard or mouse or to connect a dongle for use in wirelessly connecting various wireless-enabled peripherals. Such additional interfaces also can include serial interfaces such as, for example, an interface to connect to a ribbon cable. It should also be appreciated that the various system components can be electrically coupled to communicate with the computing device 720 over one or more of a variety of suitable interfaces and cables such as, for example, USB interfaces and cables, ribbon cables, Ethernet cables, among other suitable interfaces and cables.

The data signals output by the image sensors may in some implementations be multiplexed, serialized or otherwise combined by a multiplexer, serializer or other electrical component of the imaging system before being communicated to the computing device. In certain implementations, the computing device can further include a demultiplexer, deserializer or other device or component for separating the image data from each of the image sensors so that the image frames can be processed in parallel by the one or more processors.

Some of the CACAO-FP systems shown in FIGS. 8, 10, and 11 have one or more components that are similar to those described with respect to CACAO-FP system 700 in FIG. 7.

Although many implementations of the CACAO-FP system are described as imaging a sample that is assumed to be stationary, the embodiments disclosed herein are not so limited. For example, in one implementation, a CACAO-FP system, e.g., the CACAO-FP system 700, the CACAO-FP system 1000, or CACAO-FP system 1100, also includes a motion correction arm for tracking motion of a moving sample. The motion correction arm includes an additional imager and optical components of the optical system that are configured to propagate light reflected from the sample to the additional imager. An example of a motion correction arm is the second imager 351 and lens 336 of the pupil ptychography imaging system 300 shown in FIG. 3. In this implementation, the optical system further includes one or more optical components configured to propagate light from the illuminated sample to the additional imager. The additional imager is then configured to acquire a plurality of unmodulated images of the moving sample. In one aspect, the unmodulated images can be acquired in parallel with acquiring the plurality of modulated images (limited aperture images and/or variably-coded aperture images) based on apertures at the Fourier domain. In this example, the parallel sequence of unmodulated-aperture images is used for image registration of the modulated images for motion correction. A motion registration operation that can be used is operation 530 in FIG. 5.

FIG. 8 is a schematic diagram of certain optical elements of a CACAO-FP system 800, according to various implementations, and an unknown lens 814 with a focal length f₀ and a sample with a spatially incoherent field 812 at a sample plane 811. It would be understood that the schematic diagram is simplified for the purpose of illustrating the general optical scheme of the CACAO-FP system 800, and does not show all system components. The CACAO-FP system 800 includes an optical system having a first lens 830 a with a focal length f₁, a second lens 830 b with a focal length f₂, and a third lens 830 c with a focal length f₃. The CACAO-FP system 800 also includes a first image plane 831 a. The first lens 830 a, second lens 830 b, and third lens 830 c are configured to relay the image from the unknown lens 814 and sample to an imager (not shown) at the second image plane 831 b. The distance d is an arbitrary distance smaller than f₃. The images captured by the imager are intensity only images. The unknown lens 814 is a representation of aberrating medium between the sample plane and the first lens 830 a. In a retinal imaging example, the unknown lens 814 would represent the lens and cornea. The CACAO-FP system 800 also includes an aperture modulator 832, shown at this instant providing a limited aperture 833 at the pupil plane. The CACAO-FP system 800 is configured to determine the sample-induced aberration characteristics of the unknown lens 814 and the aberration in the optical system and to correct for both.

FIG. 9 is the general imaging pipeline for a CACAO-FP imaging method, according to various implementations. At a tiling operation 910, the sample plane, which has coordinates (x,y) is divided into a plurality of tiles. The tiles are considered to be isoplanatic patches with aberration assumed to be spatially invariant within each of the tiles. Each of the tiles is processes on its image plane, which has coordinates (ξ, η), to recover a higher resolution tile image i.e. having higher resolution than the raw intensity images captured by the imager.

In certain implementations, during an a data acquisition phase, the imager of a CACAO-FP system captures: (i) a plurality of limited-aperture images while the aperture modulator generates smaller limited apertures which collectively span the desired full pupil, (ii) a plurality of variably-coded aperture images while the aperture modulator modulates a plurality of coded apertures with different patterns (also sometimes referred to herein as “variably-coded apertures”) at the pupil plane; and (iii) a full circular aperture while the aperture modulator generates the desired full pupil. The images captured encode the sample-induced and optical system aberration in their point spread function. During the image construction phase, the point spread functions can be extracted, e.g., using a blur estimation operation as known to those of skill in the art. These intensity values of the spatially filtered pupil function are synthesized into a full pupil function with a Fourier ptychographic process described in FIG. 6.

Returning to FIG. 9, the m^(th) small mask (also referred to herein as m^(th) limited aperture) is labeled W_(m)(u, v), the point spread function (PSF) associated with the m^(th) small mask for the isoplanatic patch t is labeled b_(m,t)(ξ, η), and the associated limited-aperture tile image captured with the m^(th) small mask is i_(m,t) (ξ, η), respectively. Also, the n^(th) large mask (also referred to herein as n^(th) coded aperture) is labeled A_(n)(u, v), the point spread function (PSF) associated with the n^(th) large mask for the isoplanatic patch t is labeled h_(m,t)(ξ, η), and the associated coded-aperture tile image captured with the n^(th) large mask is ϕ_(n,t)(ξ, η), respectively.

At operation 920, the CACAO-FP imaging method performs a portion of the data acquisition process by acquiring a plurality of m limited-aperture images as illustratively represented by the row of three limited-aperture images being acquired at the top for the purpose of illustration. Each of the limited-aperture images is tiled into a plurality of limited-aperture tile images, i_(m,t)(ξ, η). During operation 920, the imager captures the plurality of m limited-aperture images while the aperture modulator generates a plurality of circular apertures, which collectively span the full pupil e.g. full pupil of the unknown lens 814 shown in FIG. 8.

At operation 920, the CACAO-FP imaging method also performs a portion of the image reconstruction process by determining the local point spread functions (PSFs) of the m limited-aperture images b_(m,t)(ξ, η), e.g., using the blur estimation procedure illustrated by the flowchart 1400 shown in FIG. 14, and then the PSFs of the m limited-aperture images are synthesized into a full-aperture pupil function using the Fourier ptychographic process described in FIG. 6.

It would be understood that the CACAO-FP imaging method performs the operations of the data acquisition process and then the operations of the image reconstruction process in certain implementations described herein. Also, it would be understood that although the data acquisition process of certain implementations is described in certain orders, e.g., first acquiring a plurality of limited-aperture images, then a plurality of coded-aperture images, and then a full aperture image, the disclosure is not so limiting and other orders are included e.g., a full aperture image, the limited-aperture images, and then the coded-aperture images or the full aperture image, the coded-aperture images, and then the limited-aperture images, etc.

At operation 930, the CACAO-FP imaging method performs a portion of the data acquisition process by acquiring a full aperture image (illustratively represented by top row, left image) and a plurality of n variably-coded-aperture images (illustratively represented by top row, right image). The imager captures the variably-coded-aperture images while the aperture modulator generates code apertures with various patterns. Each of the variably-coded-aperture images is tiled into a plurality of variably-coded-aperture tile images, ϕ_(n,t)(ξ, η). During operation 930, the imager captures the plurality of n coded-aperture images while the aperture modulator generates a plurality of coded apertures respectively.

At operation 940, the CACAO-FP imaging method also performs a portion of the image reconstruction process by using the recovered pupil function from operation 920 and the coded-aperture images to recover the aberration-free intensity distribution of the sample o_(t)(x,y) using a deconvolution operation such as, e.g., described in FIG. 13. Some discussion of the CACAO-FP imaging pipeline shown in FIG. 9 can be found in Chung, J., Martinez, G. W., Lencioni, K. C., Sadda, S. R., Yang, C.,” Computational aberration by coded-aperture-based correction of aberration obtained from optical Fourier coding and blur estimation (May 2019), which is hereby incorporated by reference in its entirety.

FIG. 10 is a schematic diagram of components of a CACAO-FP system 1000, according to one implementation. The CACAO-FP system 1000 is shown at an instant during operation when imaging an uneven 2D sample 1011 on a slide 1016. At this instant, illumination is provided by a condenser 1005 for incoherent illumination (e.g., monochromatic LED) at a desired wavelength (e.g., 520 nm). For a sample with fluorescence signals, the illumination is at the excitation wavelength of the fluorophores. In the case of a thick fluorescent sample that needs to be scanned along the z-axis (e.g. CLARITY samples), a light sheet beam can be used as the excitation illumination to allow a plane of fluorophores to fluoresce, one plane at a time.

The CACAO-FP system 1000 includes an optical system with an objective lens 1030 a, a first relay lens 1030 b, a second relay lens 1030 c, a polarized beam-splitter 1030 d, a polarizer 1030 e, and a tube lens 1030 f. The CACAO-FP system 1000 also includes an imager 1040 (e.g., camera) and an aperture modulator 1032 in the form of a reflective spatial light modulator. The aperture modulator 1032 is configured to modulate reflective apertures at the Fourier plane of the imager 1040 and the imager is synchronized to capture modulated images. The aperture modulator 1032 and imager 1040 are configured so that the imager 1040 acquires: (i) a plurality of limited-aperture images and (ii) a plurality of coded-aperture images. In one case, the aperture modulator 1032 and imager 1040 are further configured so that the imager 1040 acquires (iii) a full aperture image. The optical system is configured to propagate light transmitted through the sample 1011 to the aperture modulator 1032 and from the aperture modulator 1032 to the first imager 1040. The first relay lens 1030 b and the second relay lens 1030 c have the same focal length (e.g., 100 mm). An example of a suitable pair of relay lenses are the AC508-100-A lenses from Thorlabs Inc.®. An example of a suitable beam splitter is the polarized beam splitter AC508-100-A from Thorlabs Inc.®.

The polarized beam splitter 1030 d lies in front of the aperture modulator 1032 to enable binary modulation of the aperture modulator 1032. A polarizer 1030 e is placed after the polarized beam-splitter 1030 d to filter the polarized light to compensate for the low extinction ratio in reflection of the polarized beam-splitter 1030 d. The tube lens 1030 f Fourier transforms the modulated light and images it on the imager 1040. An example of a commercially-available polarized beam splitter that can be used is the polarizing beam splitter PBS251 available from Thorlabs Inc.®. A polarizing beam splitter is designed to reflect a component of the light with a particular polarization direction (e.g. 0 degrees) while transmitting a component with the perpendicular polarization direction (e.g. 90 degrees).

During operation, the imager 1040 captures the image of the sample 1011 with the pupil (aperture) defined by the patterns on the display of the aperture modulator 1032 in the imager's Fourier plane. The aperture modulator 1032 displays an aperture on the camera's Fourier plane during each image capture. During the CACAO-FP imaging method, the images are processed using Fourier Ptychography as described in the following section C to construct the pupil function that contains aberration induced by the sample and the optical system. Deconvolution is performed on the plurality of coded-aperture images captured while various coded apertures are displayed on the aperture modulator 1032 to produce an aberration-removed image of the sample.

Although various implementations are described in transmission mode with illumination transmitted through the sample being imaged, other implementations can be in reflection mode. For example, the condenser 1005 in FIG. 10 can be placed on the same side of the slide 1016 as the collection lens 1030 a for an implementation in reflection mode.

During an exemplary image acquisition process of the CACAO-FP imaging system 1000, the sample is illuminated by a light source. In one example, the sample is illuminated by a monochromatic light source such as an LED light source (e.g., 520 nm, UHB-Microscope-LED-520 made by Prizmatrix®) filtered with a 10 nm bandpass filter. The aperture modulator 1032 displays a full aperture, a plurality of coded apertures, e.g., rotated at 0 degrees, 45 degrees, 90 degrees, and 135 degrees with the maximum diameter matching the full aperture, and a plurality of limited apertures (e.g., circular apertures) shifted to different positions within the full aperture dimension. For example, the limited apertures may be shifted in a spiraling-out pattern. The exposure of the imager 1040 is synchronized with the aperture modulator 1032 to take a full aperture image, a plurality of m coded-aperture images, and a plurality of n limited-aperture images. In one aspect, n is in a range between about 30 to about 60. In another aspect, n is in a range between about 100 to about 200. In one aspect, n is greater than 100. In one aspect, m can be in a range between about 30 to about 60. In another aspect, m can be in a range between about 100 to about 200. In one aspect, m is greater than 100.

In one implementation, each of the images corresponding to one of the apertures is captured multiple times by the imager of a CACAO-FP system and the image data is summed together to increase the signal-to-noise ratio.

According to various implementations, a CACAO-FP system implements one or more processors (internal/external) to interpret and process the image data sampled during an image acquisition cycle to generate processed image data. In some implementations, the processor(s) are configured or configurable to perform operations on the image data to synthesize the spatially varying system- and sample-induced aberration using Fourier ptychography techniques, and remove the aberration using deconvolution to obtain substantially aberration-free images of the sample. In one aspect, the aberration-free or substantially aberration free image is a fluorescence image.

FIG. 11 is a schematic diagram of components of a CACAO-FP system 1100, according to a light sheet fluorescence microscopy implementation. The CACAO-FP system 1100 is shown at an instant during operation when imaging a clarity sample 1111. At this instant, a galvo and laser system 1105 and lens 1108 (e.g. lens with a focal length of 40 mm) configured to provide a light sheet beam of excitation illumination into the clarity sample 1111. The light sheet beam can cause a plane of fluorophores to fluoresce, one plane at a time. The CACAO-FP system 1100 includes an optical system having an a first lens 1130 a which is an objective lens, a filter wheel 1130 b, a second lens 1130 c (e.g. lens with a focal length of 150 mm), a mirror 1130 d, a third lens 1130 e (e.g. lens with a focal length of 100 mm), a polarized beam splitter 1130 f, an aperture modulator 1132, a polarizer 1130 g, and a fourth lens 1130 h (e.g. lens with a focal length of 300 mm). The CACAO-FP system 1100 also includes an imager 1140 (e.g., light sheet camera such as Hamamatsu Flash 4.0 ®). The first lens 1130 a is configured to receive fluorescence emissions from the clarity sample 1111. The filter wheel 1130 b is configured to allow for selecting different emission filters to be placed in the optical path between the second lens 1130 c and the first lens 1130 a to selectively pass emissions of a particular wavelength, for example, to capture multiple fluorescence color images. The second lens 1130 c, the mirror 1130 d, and the third lens 1130 e propagate the emissions to the aperture modulator 1132. The aperture modulator 1132 is configured to modulate reflective apertures at the Fourier plane of the imager 1140 and the imager is synchronized to capture modulated images. The aperture modulator 1132 and imager 1140 are configured so that the imager 1140 acquires: (i) a plurality of limited-aperture images and (ii) a plurality of coded-aperture images. In one case, the aperture modulator 1132 and imager 1140 are further configured so that the imager 1140 acquires (iii) a full aperture image. The polarized beam splitter 1130 f lies in front of the aperture modulator 1132 to enable binary modulation of the aperture modulator 1132. A polarizer 1130 g is placed after the polarized beam-splitter 1130 f to filter the polarized light to compensate for the low extinction ratio in reflection of the polarized beam-splitter 1130 f. The fourth lens 1130 h Fourier transforms the modulated light and images it on the imager 1140. A polarizing beam splitter is designed to reflect a component of the light with a particular polarization direction (e.g. 0 degrees) while transmitting a component with the perpendicular polarization direction (e.g. 90 degrees).

During operation, the imager 1140 captures the image of the sample 1111 with the pupil (aperture) defined by the patterns on the display of the aperture modulator 1032 in the imager's Fourier plane. The aperture modulator 1032 displays an aperture on the camera's Fourier plane during each image capture. During the CACAO-FP imaging method, the images are processed using Fourier Ptychography as described in the following section C to construct the pupil function that contains aberration induced by the sample and the optical system. Deconvolution is performed on the plurality of coded-aperture images captured while various coded apertures are displayed on the aperture modulator 1032 to produce an aberration-removed image of the sample.

C. CACAO-FP Methods

1. Image Acquisition

In the CACAO-FP image acquisition, a point on the sample s(x,y) propagates to the imager plane. On the sample plane, a unit amplitude point source at (x₀, y₀) can be described by:

$\begin{matrix} {{{U_{0}\left( {x,{y;x_{0}},y_{0}} \right)} = {\delta\left( {{x - x_{0}},{y - y_{0}}} \right)}},} & \left( {{Eqn}.\mspace{14mu} 1} \right) \end{matrix}$

In Eqn. 1, U₀ (x, y; x₀, y₀.) refers to the complex field of the point on the sample plane and δ (x−x₀, y−y₀) is the Dirac delta function describing the points located at (x₀, y₀). The Fresnel propagation is used to propagate it to the plane of the unknown lens (e.g., lens 814 in FIG. 8) and the phase delay caused by the unknown lens is applied, assuming an idealized lens with the estimated focal length f₀. Any discrepancy from the ideal is incorporated into the pupil function P(u, v; x₀, y₀.), which is typically considered a circular bandpass filter with a uniform modulus and some phase modulation. The field right after passing through the unknown lens is

$\begin{matrix} {{U_{p}\left( {u,{v;x_{0}},y_{0}} \right)} = {{P\left( {u,{v;x_{0}},y_{0}} \right)}{{\exp\left\lbrack {{- j}\frac{2\;\pi}{\lambda\; f_{0}}\left( {{x_{0}u} + {y_{0}v}} \right)} \right\rbrack}.}}} & \left( {{Eqn}.\mspace{14mu} 2} \right) \end{matrix}$

In Eqn. 2, λ is the wavelength of the field and (u, v) are the coordinates of both the plane right after the end lens and the aperture plane of the CACAO-FP system as these planes are conjugate to each other. The aperture plane is sometimes referred to herein as the pupil plane for this reason. The spatially varying nature of the aberration of the unknown lens (i.e., the sample-induced aberration) is captured by the pupil function's dependence on (x₀, y₀).

During a tiling operation, the sample is divided into t small tiles of isoplanatic patches (e.g., t=1, 2, 3, 4, . . . ) on the sample plane contains (x₀, y₀) and other points such that the spatially varying aberration can be assumed to be constant. The field emerging from the unknown lens is essentially its pupil function with the additional phase gradient terms defined by point sources location on the sample plane.

At the pupil plane, the coded aperture (aperture mask) M(u, v) is applied to produce:

$\begin{matrix} {{{U_{F}^{\prime}\left( {u,{v;x_{0}},y_{0}} \right)} = {{M\left( {u,v} \right)}{P_{i}\left( {u,v} \right)}{\exp\left\lbrack {{- j}\frac{2\;\pi}{\lambda\; f_{0}}\left( {{x_{0}u} + {y_{0}v}} \right)} \right\rbrack}}},} & \left( {{Eqn}.\mspace{14mu} 3} \right) \end{matrix}$

After propagation to the imaging plane, the intensity pattern i_(PSF,t)(ζ, η) describing the mapping of a point on the sample to the imager plane is as follows:

$\begin{matrix} {i_{PSF},{\left( {\xi,{\eta;x_{0}},y_{0}} \right) = {{{\mathcal{F}\left\{ {{M\left( {u,v} \right)}{P_{i}\left( {u,v} \right)}} \right\}\left( {\xi,\eta} \right)*{\delta\left( {{\xi + \frac{x_{0}}{\lambda\; f_{0}}},{\eta + \frac{y_{0}}{\lambda\; f_{0}}}} \right)}}}^{2} = {{b_{i}\left( {{\xi + \frac{x_{0}}{\lambda\; f_{0}}},{\eta + \frac{y_{0}}{\lambda\; f_{0}}}} \right)}.}}}} & \left( {{Eqn}.\mspace{14mu} 4} \right) \end{matrix}$

Where in Eqn. 4, b_(t)(ξ, η)=|F{M(u, v)P_(t)(u, v)}(ξ, η)|² is the intensity of the PSF of the combined system in FIG. 8 for a given coded aperture M(u, v) and within the isoplanatic patch t. From Eqn. 4, PSFs for different point source locations are related to each other by simple lateral shifts such that image i(ζ, η) captured by the system with the unknown sample-induced aberration within the isoplanatic patch s_(t)(x,y) be represented by:

$\begin{matrix} {{{i_{i}\left( {\xi,\eta} \right)} = {{{b_{i}\left( {\xi,\eta} \right)}*{{s_{t}\left( {\xi,\eta} \right)}}^{2}} = {{b_{i}\left( {\xi,\eta} \right)}*{o_{i}\left( {\xi,\eta} \right)}}}},} & \left( {{Eqn}.\mspace{14mu} 5} \right) \end{matrix}$

In Eqn. 5. o_(t)(ζ, η) is the intensity of s_(t)(ζ, η), * is the convolution operator and coordinate scaling is ignored. Based on Eqn. 5, the image captured by the imager is a convolution of the sample's intensity field with a PSF associated with sub-region of the full pupil function which can be defined by a coded or limited apertures at the pupil plane. Thus, the CACAO-FP system can capture aperture images of the sample under the influence of PSFs that originate from different sub-regions of the pupil. The apertures of varying shapes and sizes, e.g., coded apertures and limited apertures, of the pupil function can be used to reconstruct the pupil function.

2. Flowcharts

In various implementations a CACAO-FP imaging method includes one or both of a data acquisition phase and an image reconstruction phase. A discussion of the general imaging pipeline of a CACAO-FP imaging method of various implementations is described above with reference to FIG. 9. During the data acquisition phase, the imager captures: (i) a plurality of limited-aperture images while the aperture modulator generates limited apertures which collectively span the desired full pupil, (ii) a plurality of coded-aperture images while the aperture modulator modulates a plurality of variably-coded apertures with different patterns at the pupil plane; and (iii) a full aperture while the aperture modulator generates the full pupil. These operations can be performed in any order. During the image reconstruction phase, the plurality of limited-aperture images are used for pupil function reconstruction and the sample- and system-induced aberration is removed from the full- and coded-aperture images.

Generally, the aberration induced by a sample is not the same for different regions in the field-of-view, e.g., when 1) the sample is uneven, 2) the features of interest are embedded behind the refractive index inhomogeneity that is different from features located in other regions, or 3) both 1 and 2. For this reason, the field-of-view is divided into tiled regions in certain implementations described herein.

In various implementations, the image reconstruction phase includes a tiling operation during which all the captured images ((i) the plurality of limited-aperture images, (ii) the plurality of coded-aperture images, and (iii) the full aperture) are divided into tile images within which the aberration is assumed constant and the aberration characterization procedure described below is applied for each tile image. One of the limited-aperture images is used as a ground-truth. This limited-aperture image is used to deconvolve all the limited-aperture images to recover the point-spread function (PSF) associated with each limited aperture. These PSFs are the intensity information of the variously low-pass filtered versions of the actual complex PSF of the system with the full aperture opened. A phase retrieval algorithm is used to synthesize the low-passed PSFs into the full-sized complex pupil function. Various phase retrieval algorithms can be used to solve this problem such as the one mentioned in Zheng, G., Horstmeyer, R. and Yang, C., “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photonics, (2013), which is hereby incorporated by reference in its entirety. One implementation of phase retrieval that can be used to recover the pupil function of the optical system of a CACAO-FP system given the spatially incoherent images captured by the system is described in the flowchart 600 shown in FIG. 6. After reconstructing the complex pupil function, the PSF associated with it can be calculated, which can then be used to deconvolve from the full- and coded-aperture images to obtain aberration-removed images of the sample. An example of a process that can be used to deconvolve is described in the flowchart shown in FIG. 13. FIG. 13 depicts a flowchart 1300 of operations of an example of a deconvolution process with iterative Tikhonov regularization, according to one aspect.

FIG. 12 depicts a flowchart 1200 of operations of a CACAO-FP imaging method performed by a CACAO-FP system such as any of the CACAO-FP systems described herein, according to various implementations. For example, one or more processors and memory of a CACAO-FP system may perform certain image reconstruction operations.

At operation 1210, the CACAO-FP method captures: (i) a plurality of m limited-aperture images while the aperture modulator generates m limited apertures which collectively span the full pupil (e.g., overlapping circular apertures which collectively cover the full pupil), (ii) a plurality of n coded-aperture images while the aperture modulator modulates a plurality of variably-coded apertures with n different patterns at the pupil plane; and (iii) a full aperture while the aperture modulator generates the full pupil. These acquisition operations can be performed in any order. In one implementation, N is in a range between about 30 and about 60. In another implementation, N is in a range between about 100 and about 200. In another implementation, N is greater than 100. In some cases, the number N is selected based on the severity of the aberration. In one implementation, M is in a range between about 2 and about 10. In another implementation, M is in a range between about 20 and about 100. In another implementation, M is greater than 10. In another implementation, M is greater than 100. In another implementation, M is 1. In one implementation, the aperture modulator is a LCoS device that can provided a plurality of coded apertures by rotating at different degrees, e.g., at 0 degrees, 45 degrees, 90 degrees, and 135 degrees. In other implementations, the aperture modulator may be another fast switching amplitude modulation device (e.g., a DMD, if the incidence and reflection angle is normal to the DMD surface). In one implementation, the aperture modulator provides a plurality of limited apertures by providing a circular aperture at different locations covering, by overlapping aperture regions, the full aperture dimension in a spiraling-out pattern.

In one aspect, the coded apertures are designed to maximize the OTF's spatial frequency content's modulus. The coded aperture patterns are selected depending on the amount of noise in the imaging condition.

At operation 1220, the CACAO-FP method performs an optional tiling operation (denoted by dashed line). At the tiling operation, the image data of each of the full field-of-view images captured in operation 1210 at the sample plane is divided into a plurality of tile images. Each of the images captured in operation 1210 is tiled into a plurality of limited-aperture tile images. The tiles are considered to be isoplanatic patches and the aberration within each of the tile images assumed to be spatially invariant. Each of the tiles is processed on its image plane to recover a higher resolution tile image in the following operations. In one implementation, the field-of-view may be segmented into equivalent tile portions based on keeping each portion less than a size within which the aberration can be assumed to be constant. In one implementation, the field-of-view may be segmented to keep the field of view of each tile image within a predetermined size (e.g., 1 degree, 2 degrees, or 3 degrees of visual field). In one aspect, the number of tiles is in a range between about 30 and about 60. In another implementation, the number of tiles is greater than about 100. In another implementation, the number of tiles is greater than about 200. In another implementation, the number of tiles is less than 30. In one implementation, the images acquired in operation 1210 can be assumed to have a constant aberration and this operation 1220 can be omitted and each image the operations below recover a single higher resolution image. In other implementations where the images are assumed not to have a constant aberration, this operation 1220 is employed and the operations below recover higher resolution tile images. For purposes of illustration, the below operations 1240 and 1250 are discussed as though the optional tiling operation has been performed.

At operation 1210, the CACAO-FP imaging method also performs a portion of the image reconstruction process by determining the local point spread functions (PSFs) of the m limited-aperture images b_(m,t) (ξ, η), e.g., using the blur estimation procedure illustrated by the flowchart shown in FIG. 14, and then the PSFs of the m limited-aperture images are synthesized into a full-aperture pupil function using the Fourier ptychographic process described in FIG. 6.

At operation 1230, the CACAO-FP method characterizes the sample-induced and system-induced aberration using image data of the images collected in operation 1230. If each of the captured images were tiled in the optional operation 1220, then operation 1230 is performed to determine an aberration based on each of the tile regions. To characterize the sample-induced and system-induced aberration, the local point spread functions (PSFs) of the m limited-aperture images b_(m,t)(ξ, η) is recovered and then the recovered PSFs of the m limited-aperture images are synthesized into a full-aperture pupil function using a Fourier Ptychography-based alternating projections process described in FIG. 6. In one implementation, the blur estimation process described in the flowchart 1400 shown in FIG. 14 is used to determine the local PSF for each limited-aperture tile image. FIG. 14 depicts a flowchart of operations of an example of a blur estimation process for determining local PSFs from limited-aperture images, according to one aspect.

FIG. 6 depicts a flowchart 600 that describes details of an example of sub-operations of operation 1230. In Section I above, the flowchart 600 is described with reference to a pupil ptychography example. It would be understood that these sub-operations can also be employed by a CACAO-FP example where n is the number of limited-aperture images. For example, at operation 602, the CACAO-FP method deconvolves each of the plurality of n limited-aperture images based on a ground truth image to obtain an incoherent point-spread-function PSF. In one case, one of the limited-aperture images is used as the ground truth image. At operation 604, the CACAO-FP method initializes a full-aperture pupil function e.g., with is inside the passband and 0s outside the passband. The pass band is defined by the full aperture NA in the Fourier domain. At operation 606, the CACAO-FP method initializes the counter i=1. The incoherent point-spread-functions of the M limited aperture images are the intensity information of the various low-pass filtered versions of the actual complex point spread function of the optical system with the full aperture opened. At operation 608, the CACAO-FP method determines the low-pass filtered version of the full-aperture pupil function, P(k_(x),k_(y)), with a limited aperture, B_(i)(k_(x),k_(y)), that corresponds to the incoherent point-spread-functions, o_(i)(x, y). Then, the low-pass filtered version with a limited aperture, B_(i)(k_(x),k_(y)), is Fourier transformed to obtain the coherent point-spread-function p_(i)(x, y) according to: p_(i)(x, y)=F{B_(i)P}. The incoherent PSF is the absolute squared of the coherent point spread function. At operation 610, the method replaces the amplitude of p_(i)(x, y) with the square root of the incoherent point-spread-function value, o_(i)(x, y) using:

$p_{i}^{\prime} = {\sqrt{o_{i}}{\frac{p_{i}}{p_{i}}.}}$ At operation 612, the method updates the corresponding region of the full-aperture pupil function, P(k_(x),k_(y)), with P_(i). P_(i) is the Fourier transform of p′_(i) according to: Pi=F{p′_(i)}. At operation 614, the method increments the counter i=i+1. At operation 616, the method returns to repeat operations 608, 610, 612, 614 until i is greater than N. If i is greater than Nat operation 610, then the method goes on to operation 618 to determine whether the solution has converged. If it is determined that the solution has not converged at operation 618, the method returns to operation 606 to initialize the counter to i=1. If it is determined that the solution has converged at operation 618, the method has reconstructed the solution for the pupil function P(k_(x),k_(y)) at operation 620. The method determines the aberration for the full-aperture image based on the reconstructed pupil function P(k_(x),k_(y)). If the operational tiling operation was performed on the image, the method determines the aberration for each tile image based on the reconstructed pupil function P(k_(x),k_(y)) for the tile region.

Returning to FIG. 12, at operation 1240, the CACAO-FP method deconvolves the full aperture image to correct for the sample-induced and system-induced aberration. At operation 1240 at operation 1240, the recovered pupil function from operation 1230 and the n coded-aperture images acquired at operation 1210 are used to recover the aberration-free intensity distribution of the sample o_(t)(x,y) using a deconvolution process such as, e.g., the deconvolution process in the flowchart 1300 described in described in FIG. 13. The aberration-free or substantially aberration-free tile images are moscaiced together to form a full field-of-view image that is aberration-free or substantially aberration free. If each of the captured images were tiled in the optional operation 1210, then operation 1240 decolvolves each of the tile images of the full aperture image to correct for aberration in each tile region. In one aspect, the aberration-free or substantially aberration free image is a fluorescence image.

In one implementation, sample movement is also accounted for in the CACAO-FP method. In this case, the CACAO-FP method includes the operations of flowchart 1200 and additionally includes the motion correction operation 530 shown in FIG. 5 as applied to a CACAO-FP system that includes the motion correction arm and also includes an addition acquisition of unmodulated images at operation 1210.

Certain implementations pertain to computationally aberration compensating imaging systems and methods such as, e.g., pupil Ptychography systems and methods and CACAO-FP method systems and methods.

Modifications, additions, or omissions may be made to any of the above-described embodiments without departing from the scope of the disclosure. Any of the embodiments described above may include more, fewer, or other features without departing from the scope of the disclosure. Additionally, the steps of the described features may be performed in any suitable order without departing from the scope of the disclosure.

It should be understood that the present invention as described above can be implemented in the form of control logic using computer software in a modular or integrated manner. Based on the disclosure and teachings provided herein, a person of ordinary skill in the art will know and appreciate other ways and/or methods to implement the present invention using hardware and a combination of hardware and software.

Any of the software components or functions described in this application, may be implemented as software code to be executed by a processor using any suitable computer language such as, for example, Java, C++ or Perl using, for example, conventional or object-oriented techniques. The software code may be stored as a series of instructions, or commands on a CRM such as a random access memory (RAM), a read only memory (ROM), a magnetic medium such as a hard-drive or a floppy disk, or an optical medium such as a CD-ROM. Any such CRM may reside on or within a single computational apparatus, and may be present on or within different computational apparatuses within a system or network.

Although the foregoing disclosed embodiments have been described in some detail to facilitate understanding, the described embodiments are to be considered illustrative and not limiting. It will be apparent to one of ordinary skill in the art that certain changes and modifications can be practiced within the scope of the appended claims.

One or more features from any embodiment may be combined with one or more features of any other embodiment without departing from the scope of the disclosure. Further, modifications, additions, or omissions may be made to any embodiment without departing from the scope of the disclosure. The components of any embodiment may be integrated or separated according to particular needs without departing from the scope of the disclosure. 

What is claimed is:
 1. A computationally aberration compensating imaging system comprising: an imager; an optical system comprising an aperture modulator configured to modulate apertures at a Fourier plane of the imager, and one or more optical elements configured to propagate incoherent light from a sample being imaged to the aperture modulator and propagate light from the aperture modulator to the imager, wherein the imager is configured to acquire a plurality of coded-aperture images, a plurality of limited-aperture images, and a full pupil image; and one or more processors and memory configured to: use the plurality of limited-aperture images to recover a pupil function of the optical system; and coded-aperture-based correct for sample-induced and system-induced aberration by deconvolving the full pupil image and the plurality of coded-aperture images using the pupil function recovered to determine a substantially aberration-free image.
 2. The computationally aberration compensating imaging system of claim 1, wherein the one or more processors and the memory are further configured to: segment each of the limited-aperture images into a plurality of limited-aperture tile images; recover a tile pupil function for each of the limited-aperture tile images; and combine the tile pupil functions recovered to generate the pupil function of the optical system.
 3. The computationally aberration compensating imaging system of claim 1, wherein the imager is configured to acquire the full pupil image, the plurality of limited-aperture images, and the plurality of coded-aperture images while the sample is being illuminated by incoherent illumination.
 4. The computationally aberration compensating imaging system of claim 1, wherein the full pupil image, the plurality of limited-aperture images, and the plurality of coded-aperture images are acquired in transmission mode.
 5. The computationally aberration compensating imaging system of claim 1, wherein the full pupil image, the plurality of limited-aperture images, and the plurality of coded-aperture images are acquired in reflection mode.
 6. The computationally aberration compensating imaging system of claim 1, wherein the one or more processors and the memory are further configured to send control signals to the imager and to the aperture modulator to synchronize image acquisition times with apertures modulated at the Fourier plane of the imager.
 7. The computationally aberration compensating imaging system of claim 1, wherein the aperture modulator is a spatial light modulator or a digital micromirror device.
 8. The computationally aberration compensating imaging system of claim 1, further comprising a second imager in communication with the one or more processors, wherein the one or more optical elements are further configured to propagate the incoherent light from the sample to the second imager, wherein the second imager is configured to acquire, in parallel with the imager, one or more unmodulated images of the sample, and wherein the one or more processors is configured to determine the substantially aberration-free image of the sample by also correcting for motion-based aberration.
 9. The computationally aberration compensating imaging system of claim 1, wherein the one or more optical elements include an emission filter configured to pass emissions from the sample of a wavelength, wherein the substantially aberration-free image is a substantially aberration-free fluorescence image of the wavelength.
 10. The computationally aberration compensating imaging system of claim 1, wherein the one or more optical elements include a plurality of emission filters configured to selectively pass emissions from the sample, wherein the computationally aberration compensating imaging system is configured to generate a plurality of substantially aberration-free fluorescence images.
 11. The computationally aberration compensating imaging system of claim 1, wherein the substantially aberration-free image is a fluorescence image.
 12. A computationally aberration compensating imaging method comprising: receiving, from an imager, a plurality of coded-aperture images, a plurality of limited-aperture images, and a full pupil image; using the plurality of limited-aperture images to recover a pupil function of a system in an optical path between a sample being imaged and the imager; and coded-aperture-based correcting for sample-induced and system-induced aberration by deconvolving the full pupil image and the plurality of coded-aperture images using the pupil function recovered to determine a substantially aberration-free image.
 13. The computationally aberration compensating imaging method of claim 12, comprising: receiving one or more unmodulated images of the sample; and correcting the plurality of limited-aperture images for motion of the sample using the one or more unmodulated images.
 14. The computationally aberration compensating imaging method of claim 12, further comprising segmenting each of the plurality of limited-aperture images into a plurality of tile images; and wherein recovering the pupil function comprises recovering a tile pupil function for each of the tile images; and combining the tile pupil functions recovered to generate the pupil function of the system.
 15. The computationally aberration compensating imaging method of claim 12, wherein the substantially aberration-free image is a fluorescence image.
 16. The computationally aberration compensating imaging method of claim 12, wherein the full pupil image, the plurality of limited-aperture images, and the plurality of coded-aperture images are acquired in reflection mode.
 17. The computationally aberration compensating imaging method of claim 12, wherein the full pupil image, the plurality of limited-aperture images, and the plurality of coded-aperture images are acquired in transmission mode. 